I think the value of hiring more experienced folks to run social media (i.e. not an intern, someone with any amount of experience) is that they can actually point out how ridiculous this will come off, and argue against this type of tweet. It really doesn't take that much corporate self awareness to see how bad it looks to try to force TOS on free speech on a public forum.
I think you underestimate how well anyone in management actually understands this. One job had me constantly pushing back on three or more paragraphs of legal text in the damndest of places. In one case, the legal text was larger than the form itself to say "we need your email to contact you with changes related to your account".
Every time I contacted our company lawyer directly for clarification, he was always fine with the short summaries I wrote.
I was the only person in the entire process that stopped to ask if any of this was really necessary. I guess that's why I was the developer handling all most of our legal compliance. Everyone else either didn't care or had given up.