The way proof works in healthcare (you said "Medical doctors") and in biomedical research (you said "studying travel medicine") is that one cites references for ones claims, whether one is the person making a claim or disagreeing with it (which is, in itself, a type of claim).
You made the claim that "Medical doctors who study travel medicine disagree" in response to the statement that "Locals are just better at avoiding bad food," which was provide as anecdotal and not backed up by any provided research citations. That original statement didn't claim to be backed up by anything at all. I'm the one who provided anecdotal evidence in support of that claim, but that was after you indicated you were aware of evidence to refute it
I agree with your assertion that the burden of proof lies with the one making claims. Please provide proof for your claim that "doctors studying travel medicine disagree" that local residents know more about how to avoid foodborne illness than visitors. You could've simply said you didn't believe it and asked the poster if they could cite evidence, but you didn't - you alluded to evidence to the contrary.
If this is just two personal opinions that disagree and neither has any research evidence to back it up, I'm going to go with my own experience at a US medical school on a resort island for 14 years (admittedly studying and teaching something other than travel medicine), 23 years practicing in a tourist destination in New England, and a dozen years as an interested observer and more recently a part-time resident in Cozumel that leads me to accept the original claim (that "Locals are just better at avoiding bad food") as correct.
If somebody has studied this claim and found evidence to disprove it, they've published that finding. Surely you should be basing what you say on being familiar with that published finding (or a presentation at a poster session or something, in which case there'll still be a citation). Otherwise, you're just making stuff up.