Twitter purchased Gnip years ago, and it's a reseller of social media data. Companies that want all the public tweets, nicely formatted and with proper licensing, can just buy the data from Twitter directly.

I'm assuming their terms give them permission to redistribute everybody's tweets, since that's kind of the whole site. I don't know why they'd restrict themselves to doing it over the internet and not the mail, but do you have any reason to think that to be the case?

We're talking about Elon Musk. I'd be surprised if he gave a shit.