I am quite concerned that Doctors in the medical field have limited to no understanding of statistics. IMO, stats should be second nature to anyone with 200 level math courses.
0.9% are 100-200 level math problems.
0.1% are beyond that, but at that point, hopefully your 200 level skills have taught you enough to learn about solving that.
In my lifetime, I only had 1, beyond 200 level problem that required research on math to understand. And technically, it was optional, but I volunteered.
Everything else was algebra.
Regarding doctors and stats, I share your concern. But I disagree with the statement that stats should be second nature to anyone that's gone through the courses. If I've learned one thing while going deeper and deeper into stats, it's that there's a lot more nuance than I originally understood, and I'm still not there. Just when I think I have a thorough understanding of p-values and the like, I'll read some "I can't believe everyone doesn't understand THIS" blog and see that there was more to the story still again. It's hard to know what you don't know.
But if you happen to have those things without a PhD, then do apply anyway and I'm pretty sure they'll be interested.
If you don't have those things, then you may not be ready for these kinds of jobs.
There are several very successful academic and industrial CS researchers without PhDs - Simon Peyton Jones for example - so it can be done.
An exception might be if you see "Publications in top-tiered journals" as a requirement. Those positions likely actually target PhDs with relevant publications. They might overlook a lack of a PhD if you're a recognized expert in the field, of course. But I interpret this requirement as "we want an academic", and there primary job is likely research and publishing papers. A Research Scientist at AWS is not an academic, as someone at Google Brain might be, but rather someone building applied ML solutions.
To get into RS position, just know your ML/stats basics well and be proficient in SQL. Nothing super hard about getting an RS role.