With YC, the applications are closed from editing and locked down before the interviews. The application can't change at/after the interview. Also the interview is only 10-20 minutes so you don't have a lot of time to talk about legal issues etc.

Was that always the case?

Read the post:

    Kyle and Jeremy applied to YC together but Jeremy left before the YC interview.

I interpret that sentence to mean that the original application included both people but Jeremy left sometime between the original application and the interview.

Yes, and since the application lists him as a founder, and "founders" in YC context are required to have at least 10% equity, it's a reasonable assumption that he had at least that much equity on that day. It's right there in writing.

The next question is, on what day was that equity no longer his, and by what means?

If there's no documentation of that ever happening they have a genuine problem.

It depends, did a company even exist prior to yc? If not, the claim for equity is pretty shaky as there was no equity at the time.