You can normally find the ATS for a job application by taking a quick peak at the source. Most companies are using a handful of ATSs and if you check their offerings, they don't include automated rejections.
Ours asks a couple (basic) questions right before submitting the application- if anyone answers "no" to any of them we don't consider that resume.
Those questions aren't related to what is being discussed: ATSs filtering people based on the contents of their resume.
I think what essentially happens is that resumes get ranked and high priority indicated factors (like a lack of Bachelor's Degree for example) will cause a resume to end up so low in the stack that it essentially doesn't exist. I know that when my company puts up a job posting we get over 100 resumes the first day. We might look through the top 30-40 resumes a day. While the other 70 resumes haven't officially been "rejected", they effectively are, since they will never see human eyes. Maybe companies with fewer applications go through every resume, but every company I have worked at gets more resumes than a single hiring manager can realistically go through, especially if they have other responsibilities (like running their department). So the ATS ranks them and we look at 30ish per day. Manually upvoting or favoriting the ones we read that we like.
The myth/rumor that certain factors get rejected by the ATS is effectively true. Rejected might not be the correct term. But "buried" could be more appropriate. But the idea that they aren't going to be considered by humans is effectively true at large organizations that get lots of applicants.