Persuasion adds a # to the relevant statistic in question during persuasion checks, it is not separate from the attribute.
I do not see this from testing at all.
At one specific persuasion level (depending on the encounter/attribute used, which varies), attribute checks are used. If having one more PER then that, it always succeeds, despite attribute values (checked with very low values, like over 15+ attribute points lower), and if having one PER less it, it always fails, despite attribute values (checked with very high values, like 15+ attributes higher).
Please, add any examples, that can be reproduced with testing, if you think this is not correct.