The counter offer that La Doctora made was $2000 less than the list price so how can it be called greedy? If THAT is greedy, then why wouldn't they think the original list price on the house was greedy and so not even make an offer in the first place?

The fact is that everybody lists real estate higher than they expect to receive, and everyone bids lower than they can pay.
And then through the negotiation process the two parties meet in the middle. That is not playing games.

IMO, it is odd that they would respond so unreasonably to a reasonable counter offer
That would be like if you're offered a $50,000/yr job and ask for $55. They will not come back and say no you can't have $55 and now we're only offering $45. If they can't go higher, then they would just say no, $50 is all we can offer, take it or leave it.
So I'm just sayin, I don't get it.