I like to see the source for information #1, because the alpha tester agreement says otherwise. Beta tester agreement isn't out yet.
SE themselves said you could do this during the alpha. Generally, it is allowed such that you can put it on a resume and/or not have to tell a lie if someone talks to you and asks what you're doing. The agreement states you're not supposed to disclose any confidential information about the product. It doesn't explicitly state you can't acknowledge your participation. SE is not going to ban you for saying "I'm in the beta." They will however probably ban you if you say "In the beta you can do this and we're testing that and yada yada and oh here's a video of it."