Again, you're wildly speculating and are not citing the text to support your claims at all. The text says Renly outdistanced his supplies. Catelyn does not say that Stannis also outdistanced his supplies, suggesting he brought them or maintained supply chain. We can infer that Stannis did, in fact, bring supplies when none of Renly's converted men starve under his command.
Catelyn never even enters Stannis's camp so why would she comment on his supply decision that she has no knowledge on? Simply, the speculation that Stannis just so happened to have an extra 16,000 supplies hidden on him is silly. Moreover, seeing how he is practically stuck in enemy territory he is even more cut off from a supply chain. And seeing how storms delayed his fleet at Blackwater I doubt that one is able to use as practical means to supply a force from the stores of Dragonstone.
Logistics is a constant concern for Stannis and plays out in virtually every conflict
Yes, and he repeatedly fails at it for the most part. His first battle plan sees him brilliantly getting his forces trapped between two forces only to be saved by untested magical means. Next he rushes out to Blackwater while ignoring that the Lannister's still have an army in the field and that Tyrells are still opposing him. Thus, once again ending up getting caught between two armies. And his march on Winterfell is so under supplied that some of his men have started to engage in cannibalism.
Considering that GRRM (through Cat) brought up supply-lines in regard to Renly but not Stannis, I'd say that Stannis has his supplies solidly secured. It makes no sense for GRRM to raise the idea of supply lines in every Stannis arc, including this one, but handwave it away when it's convenient.
Catelyn is in Renly's camp while never entering Stannis's camp, thus there is no reason for her to commit on his camp. Martin doesn't write his characters as being all knowing thus she is of course limited in what she can commit on.
It exists to contrast the two personalities: Stannis is slow, methodical, and pays attention to detail while Renly is brash, over-eager, and thinks only about the glory of combat instead of important but less sexy issues like logistics.
Please, Renly is the one that comes up with the methodical plan to slowly besiege KL from miles away with allowing his enemies to weaken themselves by fighting each other all the while support for him increases as he puts on a show of power. Furthermore, he does this all while keeping a massive force feed and content is a massive undergoing of logistics.
In contrast, we see Stannis three times come up with the exact same poorly thought out plan to attack a fixed defense while enemy forces were in the field. First, at Storm's End where he only escapes complete destruction by magical assassin then again at Blackwater where his forces are smashed and then finally again with his plan to besiege Dreadfort until Jon talks him out of it.
If anything Renly shows himself willing to play the long game opposed to Stannis repeatedly attempting to go with a knockout punch despite that leaving him open for a counter knockout.