what do i think twitter should do?
well, it needs to be able to allow the user to determine whether it's interested in it's opinions or not, to start. as a user, i don't care what twitter thinks. i didn't subscribe to twitter, and i'm not interested in having them interfere with the content i did subscribe to. so, to begin with, as user, i should have the ability to tell twitter that i don't care what it thinks, and i don't want it to interfere with my feed, ever, at all. that is to say that it's warnings and what not should be a user-configurable setting, rather than a site-wide decision.
that would mean that doing things like disabling comments and shares should never happen, ever.
second, any opinions that twitter wishes to express should be presented in parallel to those expressed by it's users, rather than on top of them. so, rather than put a disclaimer over top of a feed item, they should present a second item in the feed for people to interact with, if they decide to - or not interact with, if they don't want to. as mentioned previously, this should be user-configurable. and, maybe you could even granularize it; i might not be interested in twitter's opinions on what is true and what isn't, but i'd be happy to remove any posts from my feed that have to do with the proselytization of any type of religion.
something like this would be a proper balance that would allow twitter the ability to express it's views without stifling the views of it's users, and while allowing it's users to decide which views it feels are more worthwhile.