Yes. That is 100% true. They used to enjoy bringing her a liberal shows at one point, but there were too many instances where she would embarrass the liberal who thought it would be easy to pin that butterfly to the board as a trophy.
Discretion being the better part of valor, I think they simply decided the potential upside of inviting her as a target to throw darts at in a public setting was outweighed by the possibility she would make them look foolish.
Now, they simply just don’t invite her. She understands how that game works, if you are a conservative writer.
I think the best example of this type of behavior against conservative writers is “Unlimited Access” by author Gary Aldrich. He experienced firsthand during the Clinton administration what happens when you try to publish something that is going to skewer the current liberal in charge, whoever that might be.
The converse of that is the wide multitude of anti-Bush or anti-Reagan writers who got plenty of invitations to various television shows as well as fawning, boot licking reviews from all of their contemporaries across the country.
Jimmy Valentine's Brother, BufordP and myself went to her very well-attended book signing in DC (sponsored by Americans for Tax Reform, Brent Bozell, Human Events, Penguin Publishing USA and WMAL) when it came out; so each of us has a signed first edition. There are a lot of Coulter haters on FR now, but when I read a book, I consider the book and what is in it independently from her often-careless sarcasm and spouting off on the air. She researches carefully, cites all her sources, and can frame a debate -- something fewer freepers seem to want to take the trouble to do any more.