I just checked my copy of the PHB. Swim skill, proficiency feats, armor section in equipment; it's there in all three places. d20SRD appears to be missing that text in the proficiency feats, which is strange. It's there in the other two, and I'm inclined to value the description of armor check penalties and the skill telling you what modifiers apply over the lack of text in the feats (being that lack of text does not preclude additions by other rules).
I was with you up until here. Just because they're willing doesn't mean they're going to forgo their saving throw. Admittedly, they're likely to, but it's not part of the rules definition of "willing", the use of "willingly" notwithstanding. "Willing" only means that you can cast spells restricted to willing targets only on them (or so the argument goes).