These statements are not true, or at least greatly overstated.
Firstly, none of these are true at all for poz people whose infections are well-controlled (i.e. undetectable or nearly so).
Secondly, even if one or both poz partner (on meds) does have a significant viral load:
Both partners' meds will work just as effectively
Having unprotected sex will not make the meds stop working
If the other partner's strain is resistant to all of the meds they are on, it is possible for them to catch it (superinfection) but because the meds are combinations, this resistance is unlikely.
Edited this to remove statement regarding likelihood of superinfection - the data are not consistent, but superinfection is a significant phenomenon, see this article: [think before following links] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3752600/
That said, the cautionary statements in the first paragraph are well-stated and worth listening to! Though @BootmanLA was talking about overall probabilities, and his statements about those are correct.