It would be no different than how "germs cause diseases" would be dismissed as not trusting in evil spirits, or the atomic hypothesis being the rantings of a madman. Presumably anything we tell them they'll have to take on faith until they can check for themselves.

And by the time they're putting up orbital telescopes to look for possible gamma ray burst candidates, I think humanity will be in a safe enough position.

There would BE a claim, for starters... Excellent point though, you'd need some additional evidence or stagecraft to impress them, which probably counts as increasing the size of the message.