Ummmm you're incorrect and
IF @pilotinstitute material says exactly that he will correct it but I believe you're taking it out of context.
Remember you said, "
Pilotinstitute.com website Part 107 course" which is focused on Part 107 Regulations. Regulations for Part 107 and ~44809 are not identical and those subtle differences are exactly where you're failing to comprehend. Regardless how your UAS is registered YES you have to follow FAA Regulations but they aren't the SAME. If you register under Commercial (P107) and you FLY under Commercial (P107) you are liable for all of Part 107 unless you are operating under a Waiver etc. If you register under the Recreational side (~44809) then you are held accountable for exactly what is noted in ~44809. The CAVEAT is if you do not follow every aspect of ~44809 you are operating under Part 107 (by default) and accountable for all of Part 107.
So yes you are "subject to FAA regulations" but which set is the key factor. Flying under Recreational ~44809 does not make your accountable for Part 107 unless you burst the protective bubble of ~44809.
Just for clarity I'm linking to the
49 USC 44809: Exception for limited recreational operations of unmanned aircraft (
which is accurate and current as of 10/19/2021)
Notice in the link above Flying Over People is not mentioned. While it COULD be mentioned in the CBO you're following, that doesn't make it mandatory for all other UAS operators who might be following a different set of rules from another CBO. The trick is, if the CBO you're citing mentions/regulates Flying Over People then you are to follow those to a "T" (otherwise you're flying under Part 107 by default) but if your CBO doesn't address Flying Over People then you're good to go so long as you are safe and follow ALL other rules pertaining to your CBO and ~44809.