Sounds like a Lee press to me. Rumor is that Richard Lee had some kind of falling out with Federal so bad mouths them all the time. If the story about Federal primers was true, the first to pull them would be Federal don't you think? Give me one good reason why they would leave a product like that out there knowing it might happen?
By the way, by the time you start putting any pressure on the primer, it's started into the primer pocket and will likely blow the pressure out the case!
The statement you make, just isn't responsible or completely true. It's not just Lee but Dillon and most others press manufacturers say not to use Federal primers. The cup material is way to soft, that's why shooters use them for reduced spring-ed guns in competition. I had a Lee Priming tool, one of those that holds 100, explode and nearly lost my eye sight with Federal LR primers in it.
Better to head the warnings than to suffer non reversible damage to your body?
My experience was exactly like what jhalcott describes above but, was definitely with Federal LR primers. The primers double stacked on the punch, in my case. If you can imagine laying on an emergency room table and having pieces of plastic and metal picked out of your eyes with a pair of tweezers for 1&1/2 hours, go ahead and use Federal primers with your progressive press.
In all fairness, I don't think the problems are with Federal, the slop needed to get the lee auto prime to work with any consistency allows two primers to be on the punch at any time. And YES, I did contact a lawyer and his findings were that Lee was aware of the problem and there was a warning issued with the tool. I no longer use Lee products but don't hold them totally responsible, just to cheaply made for my taste(chromed pot metal and plastic), and as you know you get what you pay for.