So he can speak, just as long as he doesn't provide any verifiable credentials that might actually make him credible?
There is a difference between speaking for the TSA, or any other employer, and merely speaking personally as someone with personal experience of the TSA, or any other employer. It's reasonable to prohibit anyone from falsely claiming to represent someone else when expressing a personal view. As a general rule, I don't think it's reasonable to prevent them from making factually accurate claims about employment that support their own authenticity when speaking personally.
There probably needs to be an exception to that if there really is a genuine reason to avoid identifying an individual as part of a certain organisation for security reasons. However, given the tendency of governments to exaggerate "national security" and similar arguments, it would have to be a pretty compelling case and I would suggest that employees should have to be notified of it in advance so it could be properly challenged. In any case, it's hard to see how any of this would apply to a typical front-line TSA employee.
He can speak, and he can say how he knows what he's talking about--but when he took the job he was put on notice that doing so might jeopardize his employment. (He says so in the article.) He can speak, but he also has to be prepared to take the consequences of speaking.
Perhaps, though given that the employer in this case is the government, we could debate whether or not the employment should be jeopardized in a whistle-blowing case.
Either way, I'm not sure that's what we were talking about. The GGP post suggested that the TSA should be able to stop him from even mentioning their name when expressing his opinion, not just that they should be able to fire him for expressing an opinion incompatible with remaining a TSA employee.
That is precisely the issue. He is using his employer's name to lend credibility to his personal opinion.
It's clear and in context that his account is reflective of his experience and his values. Asking him not to say "TSA" would nullify the very reason for him wishing to speak out and give rise to either a toothless account or one which obviously implicated the TSA because nobody else handles airport security in the US.
As emphatically as I support the article's author's right to his opinion, and to express it, I stop short of agreeing with your position. We absolutely have the right to express any opinion, but speech is not absolutely free.
There's the cliché example of "Yelling 'Fire!' in a crowded theater". That's illegal, and with good reason. A more compelling case of legitimately restricted "speech", however, is incitement to violence. If you're actively encouraging people to commit violence on persons or property, that shit has to stop.