B B...I think dogs can remember things to some extent, but pretty much live in the present most of the time. However, another dog's smell is probably something they "remember". Danes are not generally aggressive dogs (a damn good thing), but obviously this one and your dog have a "thing" between them. It could be stopped, but would require a bit of work, on leash, with both animals. When I brought Matrix, the Border Collie mix, home after rescuing him from the car lot I worked at, my male Terrier and he got along fine for several weeks. Rider, the Terrier, was going through his rebellious "teens" at that time...Matrix was probably at least 5 years old. I used to give them treats on the porch after they had gone out and "done their business" in the yard. Matrix started wolfing his down, then making moves to try and get Rider's treat...he let him a couple of times, then all Hell broke loose one evening. Rider clamped onto (Australian Terriers have teeth and mouths much bigger than they apppear, plus extremely strong neck muscles for killing varmits on farms...they shake them to death) Matrixs' left ear and would NOT let go, even though Matrix was lifting him off the ground by raising his head. Rider is about 16lbs, and Matrix is about 50-60lbs. I had to pry his mouth off of the ear. Some damage was done to the ear, but nothing serious. This behavior continued, though Matrix never tried to steal a treat again, for several days...it was all about establishing dominance. I finally had to put Rider in his place and let everyone know that I am the Alpha Male in the pack. They have never had a problem since.
I think Dalmations used to be "coach dogs" originally, and probably nipped horses hindquarters to keep them in line when necessary. Zeus might have thought the Dane was a horse. About the only thing that could be done at this point is to have both on a leash, and let both animals know through correction and body language, who's dominant/calm/assertive. The other dog's owners would have to be on board with it too though, and it sounds like they are attempting to defend their dog's bad behavior. It's too late now, but if your dog was harmed physically, you might have taught them a lesson by sending them a vet bill. They sound irresponsible to me...allowing a dog the size of a Great Dane to be agressive IN ANY WAY is asking for trouble, and must be dealt with immediately, in an appropriate way, of course. Knowing the two dogs had an "issue", and having agreed to what you discussed, then welshing on the aggreement, is at best inconsiderate, and at worst, just being a Prick.
I have to be cautious when introducing Rider (the male Terrier) to other male dogs, even though he's neutered. He has no idea that he's only 16 lbs. I have to really watch his body language and correct immediately...he's just not afraid of anything. You get a giant dog with that kind of attitude, and you've got a real problem on your hands.