Roger Ailes and Rupert Murdoch Fox News chief Roger Ailes, left, and Rupert Murdoch (Richard Drew/Associated Press)

Did Gretchen Carlson mean to stir up a whole bunch of bad press for her employer?

That would have been a bad career move. As virtually every profile of Fox News chief Roger Ailes notes, loyalty is the No. 1 value — or element of corruption, depending on your perspective — at the No. 1 cable-news outlet. You simply don’t take your gripes public when you work at Fox News, even if you think it’s constructive criticism.

It’s unclear whether Carlson had that imperative in mind when she hopped on Fox News Radio yesterday with colleague Brian Kilmeade, with whom she co-hosted “Fox & Friends” before moving on to a daytime slot. Here’s what was said, in part:

BRIAN KILMEADE: Guess who just walked in? If you’re watching — if you have the podcast. Gretchen Carlson’s in, dressed casual, kind of. Very nice.

CARLSON: Wait a minute. Nobody’s going to recognize me because not only am I dressed casually, I have on pants.

KILMEADE: Well, pants, what is —

CARLSON: Now, pants were not allowed on Fox & Friends, remember?

KILMEADE: Yeah, what happened with that?

CARLSON: So I have jeans on, Brian. Welcome — welcome to the new Gretchen.

The no-pants dictate will resonate with anyone who has engaged in the brain-shrinking act of watching “Fox & Friends”: In episode after episode, there is Carlson, sitting in the middle of the horseshoe couch, showing some leg for the audience. Whoever concocted the rule that exposed Carlson morning after morning knew what he (most likely) or she (less likely) was doing. There are “Fox & Friends” YouTube clips cut by fans who clearly weren’t interested in what Carlson was saying: Here’s “Gretchen Carlson upskirt leg cross 05/14/2012.” Here’s “Nicole Petallides vs. Gretchen Carlson Thick Legs Duel 1/23/13.” Here’s “Gretchen Carlson legs legs legs.”

Carlson’s statement that “pants were not allowed on Fox & Friends” is false. Kilmeade and the other guy, Steve Doocy, wore them all the time. It’s apparent from her back-and-forth with Kilmeade, however, that Carlson was eager to make her disclosure about the requirement, as she pushed the issue of pants into the conversation. The media has taken ample note, too. Politico has written it up, as have a number of other Web outlets. Just this afternoon, MSNBC had a ball with the revelation.

It’s possible that Carlson is clueless enough not to realize that the no-pants disclosure would backfire against Fox News. Cluelessness, after all, was a programmatic constant on “Fox & Friends.”

But good on her. We’ve seen this before, via Megyn Kelly and Greta Van Susteren: The women of Fox News won’t stay silent on sexism.