I vaguely recall as I think back that I think Vesper framed his whole meds issue as he was more afraid to bring his medication then him outright confirming he couldn't bring it. I'd have to dig through his zatsus to find the exact quote where he talks about it. Perhaps he was confused by what you cited regarding the website. So this could be just a case of "muh anxiety" mixed with how unplanned this trip was causing him to be a retard who bit off more then he could chew. Therefore this is a
"I thought I couldn't bring my meds, so I didn't." thing and not an absolute
"I couldn't bring my meds." Maybe his managers told him he couldn't when he asked and they misunderstood, that might be just as probable as Vesper just presuming too quickly.
I think in the end this whole situation is Vesper having an in retrospect massive retard moment if his lack of meds were the problem. So remember everyone
Or you'll end up like Grandpa Vesper.