It's a shame there's no better way to preserve a tweet than taking a screenshot -- there's no way to prove that an individual said something, save for perhaps trusting the record on archive.org
It doesn't have to be this way. Either the individual or the platform could cryptographically sign content to prove that it really happened. I guess Twitter would prefer a plausible deniability. If anyone screenshots you saying something you regret, you can just say it was forged.
I've never had my name dragged through the mud on twitter or anything but I'm super glad knowing that if I do make a mistake I can delete it rather than having it immortalised on the internet to be used as a weapon against me forever.
The blockquote is still inside the page and indexed by search engines. While many will get a blank preview, it is still immortalized on the internet and visible if you block Social Tracking / Twitter's widget.js.
Twitter itself can always prove an individual user said something. I assume they never actually delete any tweet from their system, so a proper law enforcement request can require them to verify that a particular tweet actually did originate from a handle at such and such a time & IP.
It doesn't have to be this way. Either the individual or the platform could cryptographically sign content to prove that it really happened. I guess Twitter would prefer a plausible deniability. If anyone screenshots you saying something you regret, you can just say it was forged.