So then it isn't the language they are using, or the way they are presenting it, but instead the negotiation itself.

I'm getting the same vibe here. I've had this happen to me before, when I interviewed for a smaller company, and they were literally offended that their offer wasn't the only one on the table. When I told them I already have two offers, the hiring manager very politely scolded me about it, saying that they prefer candidates who apply to their company and their company only. I usually find this type of exceptionalism very amusing and had no shame in sharing my feeling with the guy.

For the past couple of years, I noticed this trend of trying to fuck over prospective employees and drive down compensation. Of course, we can't forget the no poaching cartel for which large companies got a nice slap of the wrist, but it's the small things like:

- rejecting candidates with competing offers (like OP above) - not providing offers in writing (so that it would be hard to use a verbal offer in a negotiation) - requesting written proof of competing offers or paystubs to prove current income. - prolonging or spreading the interview process over weeks/months so that you're not able to coordinate negotiations (Google is a major offender here).