They were both traveling on the right side of the road of (based on the supplied pictures from the articles) a two way, single lane each way street, and the ambulance turned right and didn’t cross any traffic, thus the Ambulance didn’t make a illegal turn.

Okay, I'll try a second time to explain:

The ambulance did cross traffic, by definition, because the bicycle was to the right of it and counts as traffic. In order for it to not cross traffic, it would have needed to start the turn from a position far enough to the right that there would have been no space for the cyclist to be in.

Cyclists don't purposefully cram themselves into tiny spaces between cars and curbs, you know. The only reason a cyclist would enter the space between the ambulance and the curb would be if the ambulance was waaaaaaay off to the left somewhere and left a huge (several foot wide) gap that invited him in, and that's not something that is okay for a car about to make a right turn to do.

Bottom line is, it is illegal to right-hook a cyclist. If you hit a cyclist while performing a right turn, you fucked up. Full stop, end of. I don't understand why people are having difficulty understanding this concept!