The government needs mindshare and advertises just like any other entity. Just like people use Facebook to tell people not to use Facebook, the FTC may buy or use services from companies they are taking legal action against. That's not an endorsement of the practices they are fighting against; it's simply how businesses work. Facebook is where the people are; if you want people to hear your message, you take the message to Facebook. It's especially relevant in this case since their work directly benefits Facebook's users, so it would not make much sense to not have their message heard there.

Also, they settled and all is good between the FTC and Facebook.

Should government agencies who regulate telephone services not use telephones?

I don't think that's a fair analogy to use. While government regulatory agencies covering the telecommunication sector may indeed use telephones, they don't stick a recommendation to use Company A on their website... especially if they have just given Company A a simple slap on the wrist for an arguably large grievance. You may (or may not) counter by saying that Facebook is an entire market in itself that can't be ignored (which it isn't), but after viewing their Facebook page I see no additional information that I couldn't simply find on the front page of the FTC's website.

"When O when will we get regulators with some distance from those they are regulating?"

Oh, that's an easy one.

Sadly, you're right.