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Actually this makes the most sense. When users type their passwords online in order to recover the data, NSA gets those passwords the same moment. I'm pretty sure Lavabit was forced to try to trick its users into giving their passwords one more time.

I find it very suspicious that people are being rushed into a quick decision.

how do you authenticate the said person so you could allow she/he to download her/his data?

Why would you need to? The data is encrypted by the password.

Particularly weak passwords could be brute forced with a dictionary attack.

In that case, the feds already have it ...

Yes, but no doubt some of Lavabit's users are more worried about random or targeted hackers, and not so worried about the US government. No need to give everyone the data just because one group already has it.