FWIW, I got through a Ph.D. program in CS without ever having to take a stats course. I took probability theory, which is related, but not the same thing. I had to figure out stats on my own. So yes, I think you're absolutely right, but it's not just "outside of STEM" -- sometimes it's inside of STEM too.
Yes. I was, however, not arguing that every student of the field would have to understand the scientific method well. It's enough that there is a critical mass of leaders having such understanding, to ensure that students (including PhD students) work in ways that supports it.
What I was arguing was that there are almost nobody with this understanding in many fields outside stem.
As for your case, I don't know exactly what "probability theory" meant at your college. But in principle, but if it's teaching about probability density functions and how to do integration on them to calculate various probabilities, you're a long way towards a basic understanding of stats surpassing many "stats" courses taught to social science students.
I myself only took a single "stats" course before graduating, which was mostly calculus applied to probability theory, without applications such as hypothesis testing baked in. Then I went on to do a lot of physics that was essentially applied probability theory (statistical mechanics and quantum mechanics).
Around that time, my GF (who was a bit older than me) was teaching a course in scientific methodology to a class of MD students who wanted to become "real" doctors (PhD programme for Medical Doctors), and the math and logic part was kind of hard for her (physicians may not learn a lot of stats until this level, but most of the MD PhD students are quite smart). Anyway, with a proper STEM background, picking up these applications was really easy.
Since then, I've had many encounters with people from various backgrounds that try to grapple with stats or adjacant spaces (data mining, machine learning, etc), and it seems that those who do not have a Math or Physics background, or at least a quite theoretical/mathematical Computer Science or Economics background, struggle quite hard.
Especially if they have to deal with a problem that is not covered by the set of conjurations they've been taught in their basic stats classes, since they only learned to "how" but not the "why".
