The defender, now at Sunderland, was twice diagnosed with testicular cancer during his career with Celtic and moved to Everton three months after being declared in remission in May 2001.
Stubbs left Everton when his four-year contract expired in June, even though he had been offered the opportunity to lead the team he supported as a boy into their first European campaign in a decade with a one-year extension. The 33-year-old has now revealed that he rejected the offer on a point of principle, as the new contract contained a clause that would allow Everton to cancel the deal if the cancer returned.
However, Everton responded by insisting it was not the clause but the length of the contract on offer that prompted Stubbs to leave, with the centre-half seeking the two-year deal he received from Sunderland rather than the one-year extension at Goodison.
"While the very last thing anyone at Everton wishes to do is become embroiled in a public row with a player who served the club so well during his four years at Goodison Park, we feel it is essential that the record is set straight," the club's head of communications, Ian Ross, said.
"When Alan joined us from Glasgow Celtic in the summer of 2001 he was in remission after recovering from testicular cancer. A clause was inserted in Alan's contract with Everton relating to the fact that he had previously suffered from a form of cancer.
"In October of last year, Alan was made the offer of a 12-month extension to his contract. Although that contractual offer did still contain what is known as a 'special notice condition' relating to his previous medical condition, Alan asked that, as he had been in remission for a number of years, it be removed.
"The club informed both Alan and his management company that we were happy to do just that once the player had been examined by a doctor of consultant status. Although Alan indicated his willingness to undergo just such an examination he subsequently informed the club that he was seeking not a 12-month extension to his contract but a 24-month extension.
"Alan eventually decided to reject the offer of a 12-month extension and, having become a free agent, he joined Sunderland."
Stubbs, who beat the disease four years ago, had said: "It was very disappointing not to stay at Everton. I haven't said anything before now, but the reason I didn't sign again with Everton is because they wanted a clause in my contract about my cancer.
"It wasn't about money. I am not going to stand here slating everyone, criticising people. But that was the be all and end all of the reason, and I wasn't happy.
"I feel as though I did as well as anyone for four years. Suddenly, the club turn round and say: 'We will offer you a one-year deal but we want a clause in it about your cancer'. I don't see that as showing loyalty."