Can companies break their own non-compete agreement?

I signed a non-compete with my former employer, and I was the only person in the company that had knowledge in the type of work that I did. Upon my departure, one of their clients contacted me and asked me to continue to service her, since the company I left was no longer able to fulfill her needs and had stopped responding to her requests. She will continue to work with the company in other capacities as well, but wants us to communicate with each other to keep things moving along they way they had always had. Once she broke the news to my former employer, they decided to “allow” this to happen until the end of the quarter so that I may act as a “buffer” until they have found, hired and trained someone in this position, and if I continue to work with her (even if she chooses to work with me over their new employee) that they will fully enforce the non-compete at that time. Many people I have spoken to about this have said that, by them “allowing” me to work with her for the next three months that they have now waived their rights to enforce this non-compete. Is this true?