That's what i thought, though i looked around a but and it seems there's some truth to the whole "supply production-heart" thing. I know the wikis are often outdated, and that HoI3 is probably the most opaque Clauswitz game ever...but the claim i often see is that supply production is distributed equally to each core province with industry -- which explains the ridiculous supply lines with, say, Siberia's arbitrary supply lines -- but at the same time doesn't seem 100% accurate, since i often see IC provinces with no supply lines attached, or with supply lines nearby but fairly off-course (no infra bottlenecks either).
Anyway, i came across this post which explains it much better:
I've tried massively over-funding supply, but with the supply "funkyness", it's impossible to really tell what effect it has. My out-of-supply troops drift into-supply then back out all the time. Normally just annoying, but these are front-line troops, and the AI knows when you're out of supply -- that's when they attack