Holgate isn't a liar, maybe. It's irrelevant.
The FA made a conclusion beyond doubt, that in the fracas on the pitch, he misheard something. I'm not sure how they determined this beyond doubt, but they did. They also determined that there wasn't enough to prove anything against Firmino, because it wasn't really provable amidst the fracas (yet they determined beyond doubt for Holgate). At the end of the day, it was one players word against another. But the response from the FA should have absolved both of blame, determined under the same conditions. This is what they failed to do.
They should have released a statement saying they felt that Holgate had honest intent and they should have said that Firmino was also an innocent party - regardless of rose-tinted supporters, FA bias, whatever perceived agenda, this wasn't done.
I don't think there's a conspiracy, I think the FA are incredibly amateurish and as said with previous cases and the obvious inconsistencies, there's a real problem.
Call that paranoid or whatever the fuck, I really don't give a shiny shite.