Less than a week since her operation, Miss Balch, from Lancashire, tweeted a picture of her with Major Kate Philp, who lost a leg in Afghanistan, and has since trekked to the South Pole with Prince Harry.
Miss Balch has a big smile on her face in the picture. She said she was "inspired by a very amazing woman", adding that one day she hopes she "can do the same for somebody else".
The Alton Towers victim was the second person to undergo life-changing surgery.
17-year-old Leah Washington was one of the four victims airlifted to hospital following the crash
Merlin Entertainments, which owns Alton Towers, wrote to all of the 16 people involved and said that, regardless of the investigation's outcome, management accepts full responsibility and that compensation will be provided.
A spokeswoman for the company said: "Irrespective of the outcome of the current investigations into the causes of the accident, in these letters we have accepted full responsibility to those who had been injured in the accident and confirmed that we will ensure that compensation will be provided to them.
Emergency services working Tuesday evening to free trapped passengers
"We have recommended each of the injured guests or their families instruct a lawyer and submit a claim for compensation which we will ensure is dealt with swiftly and sensitively."
Merlin Entertainments said it has also been working with Health and Case Management Ltd (HCML) – a leading firm of specialist independent rehabilitation providers - to provide support for the victims.
16 Four Hurt In Alton Towers Rollercoaster Crash
The Smiler ride at an empty Alton Towers can be seen from the air as the attraction is closed to the public today following yesterday's accident on The Smiler ride. Staffordshire, England. June 3 2015. Alton Towers theme park could remain closed for days(01 of10)
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(credit:Alastair Johnstone / Newsteam)
Four Hurt In Alton Towers Rollercoaster Crash(02 of10)
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ALTON, ENGLAND - JUNE 02: Emergency services work at Alton Towers Resort where two carriages crashed today on June 2, 2015 in Alton, England. Four teenagers have have been seriously injured in a crash between two carriages on the Smiler rollercoaster ride at Alton Towers. Sixteen people were in one carriage while the other one was empty. The West Midlands Ambulance Service said of the 16 on the ride, four had serious leg injuries. (Photo by Christopher Furlong/Getty Images) (credit:Christopher Furlong via Getty Images)
Four Hurt In Alton Towers Rollercoaster Crash(03 of10)
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ALTON, ENGLAND - JUNE 02: The West Midlands Air Ambulance waits to ferry injured to hospital at Alton Towers Resort on June 2, 2015 in Alton, England. Four teenagers have have been seriously injured in a crash between two carriages on the Smiler rollercoaster ride at Alton Towers. Sixteen people were in one carriage while the other one was empty. The West Midlands Ambulance Service said of the 16 on the ride, four had serious leg injuries. (Photo by Christopher Furlong/Getty Images) (credit:Christopher Furlong via Getty Images)
Four Hurt In Alton Towers Rollercoaster Crash(04 of10)
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ALTON, ENGLAND - JUNE 02: Police is seen at the entrance of Alton Towers Resort on June 2, 2015 in Alton, England. Four teenagers have have been seriously injured in a crash between two carriages on the Smiler rollercoaster ride at Alton Towers. Sixteen people were in one carriage while the other one was empty. The West Midlands Ambulance Service said of the 16 on the ride, four had serious leg injuries. (Photo by Christopher Furlong/Getty Images) (credit:Christopher Furlong via Getty Images)
Four Hurt In Alton Towers Rollercoaster Crash(05 of10)
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ALTON, ENGLAND - JUNE 02: Emergency services work at Alton Towers Resort where two carriages crashed today on June 2, 2015 in Alton, England. Four teenagers have have been seriously injured in a crash between two carriages on the Smiler rollercoaster ride at Alton Towers. Sixteen people were in one carriage while the other one was empty. The West Midlands Ambulance Service said of the 16 on the ride, four had serious leg injuries. (Photo by Christopher Furlong/Getty Images) (credit:Christopher Furlong via Getty Images)
Four Hurt In Alton Towers Rollercoaster Crash(06 of10)
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ALTON, ENGLAND - JUNE 02: An ambulance drives past the Smiler roller coaster at Alton Towers Resort on June 2, 2015 in Alton, England. Four teenagers have have been seriously injured in a crash between two carriages on the Smiler rollercoaster ride at Alton Towers. Sixteen people were in one carriage while the other one was empty. The West Midlands Ambulance Service said of the 16 on the ride, four had serious leg injuries. (Photo by Christopher Furlong/Getty Images) (credit:Christopher Furlong via Getty Images)
Four Hurt In Alton Towers Rollercoaster Crash(07 of10)
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ALTON, ENGLAND - JUNE 02: An Air Ambulance leaves Alton Towers Resort on June 2, 2015 in Alton, England. Four teenagers have have been seriously injured in a crash between two carriages on the Smiler rollercoaster ride at Alton Towers. Sixteen people were in one carriage while the other one was empty. The West Midlands Ambulance Service said of the 16 on the ride, four had serious leg injuries. (Photo by Christopher Furlong/Getty Images) (credit:Christopher Furlong via Getty Images)
Four Hurt In Alton Towers Rollercoaster Crash(08 of10)
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ALTON, ENGLAND - JUNE 02: Ian Crabbe, director of Alton Towers gives a press conference at Alton Towers Resort on June 2, 2015 in Alton, England. Four teenagers have have been seriously injured in a crash between two carriages on the Smiler rollercoaster ride at Alton Towers. Sixteen people were in one carriage while the other one was empty. The West Midlands Ambulance Service said of the 16 on the ride, four had serious leg injuries. (Photo by Christopher Furlong/Getty Images) (credit:Christopher Furlong via Getty Images)
Four Hurt In Alton Towers Rollercoaster Crash(09 of10)
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ALTON, ENGLAND - JUNE 02: A general view of the main entrance at Alton Towers Resort on June 2, 2015 in Alton, England. Four teenagers have have been seriously injured in a crash between two carriages on the Smiler rollercoaster ride at Alton Towers. Sixteen people were in one carriage while the other one was empty. The West Midlands Ambulance Service said of the 16 on the ride, four had serious leg injuries. (Photo by Christopher Furlong/Getty Images) (credit:Christopher Furlong via Getty Images)
Alton Towers Smiler accident(10 of10)
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EDITORIAL USE ONLY File photo dated 09/05/13 of The Smiler ride at Alton Towers Resort in Staffordshire, as sixteen people have been involved in a collision between two carriages at Alton Towers amusement park's Smiler attraction. (credit:Fabio De Paola/PA Wire)