You wrote, "My gut says that I should not do it regardless of the facts and the impact on me."
Trust your gut!
I've done interviews on both sides of the table, and I haven't heard (or asked) this specific question - though it's similar to common questions along the lines of "tell me about a time you/your team faced some kind of problem and what you did to overcome that problem to achieve your goal."
If you are asked this kind of question and you respond by talking about another person's disabilities and how their disabilities made things hard for you, then I feel like the very best possible outcome you can hope for is that the interviewer might, possibly, not be offended. And a lot of interviewers definitely will be put off. So the possible downside definitely outweighs the basically non-existent upside.
Just don't do it. Interviewers asking this kind of question want to hear about positive decisions you made or actions you took, and describing the problem to them is just the set-up. Don't focus on saying negative things about a coworker or your old company or how hard things were for you - find a way to focus on telling them things you did to get through a tough situation and make things better. That's what they want to hear.
Try to think of problems/situations you could discuss that are relatively innocuous in terms of the problem, but that will give you an opportunity to play up (hopefully with a straight face!) how you innovated, or rallied the team to work together, or tactfully helped your supervisor's boss in a sensitive situation, or whatever. Ideally you might try to think through 2 or 3 various situations in advance so that they are waiting in your bag of tricks ready to use.
And I guess I'm in the camp of sticking with the truth. If I'm the interviewer, I hate feeling like a candidate is just making things up (and I definitely have had that feeling sometimes). I'd much rather have a candidate say something like "I guess I'm really fortunate that I've never had a situation where I was forced to deal with an underperforming coworker [or whatever exactly I asked about], but there was another situation where ...," and then steer the answer to something vaguely related. Examples might be something like "but there was one time when one of my coworkers was out for an extended medical leave and we got swamped with several really large new orders" or "but there was one time that one of my colleagues quit without notice and really left us scrambling to meet our deadlines." Just hypotheticals - tailor to your experiences, of course.
Whatever you go with, don't dwell on the problem and how hard it was for you - just quickly set the scene and then get to the good parts about how you/your team dove in and saved the day. And if you can do it with a straight face maybe throw in how it really felt good to get a chance to really dig in and help out the team. :-)