I have a lot familiarity with the kind of non-profit they say they are: a SSA approved Employment Network service.
Even if you were unemployed, unless you were on social security disability, you could not use their services. At all.
Even if you were fired today, it would take at least 1 year to obtain disability, and at least another 1-2 years to get an approved PASS plan to be a part of their home based business program. They would try to be the service provider for the PASS plan to basically provide you with things like a computer in order to have you work for their home based business company. In that case, they could get paid quite a bit by both the employer and SSA, and they could get paid quite a bit.
They have a link on their webpage, like most telemarketers, to have your name be put on their do-not-call list. Telemarketers are required to have that by federal law, even if they are a non-profit.
That all makes me think they didn't call you because they knew you anything about you, but that they were cold calling you... and everyone else in the proverbial phone book. Because. It's what telemarketers do.
I don't think it has anything to do with being listed as disabled at work. It is usually not legal for your employer to release that info, and they are likely smart enough to not do that even if it was legal, as they would not want to be sued for such an error. Even if your employer released that info, and even if they were about to fire you, it doesn't make sense for this agency to be calling you unless they were just cold calling everyone.
I think it is most likely you just happened to be contacted by a telemarketer that was geared for people with disabilities, but that it was not caused by anything at your job.
That's my brief assessment based on a review of the site.