Which is actually a lot more charitable than my probable interpretation of such a claim: without impressive supporting evidence, I'd be more likely to assume that anyone claiming to have Einstein's brain is full of shit and probably a crackpot.

Not only do I agree, but I can't even envision what such “impressive supporting evidence” could be. I would be extremely surprised if anyone who had more than a vague idea of what Einstein did claimed to be as smart as him with a straight face; even if someone I thought was actually in the same league as him said that, I'd assume they are in jest or out of their mind -- indeed because such a statement would pattern-match a crackpot. (IME, people who are both extremely intelligent and very arrogant may say stuff like “99.99% of the people are idiots”, but they hardly ever say “I am as smart as $famously_smart_person”.

And BTW, I don't think many laymen by “Einstein” mean “someone as smart as the 60th smartest person in my home town of 60,000” -- they usually mean “one of the friggin' smartest people ever”.