It is a persistent myth that state agencies like DNR Wildlife departments introduced coyotes. I heard many such stories over my 32 year career working as a biologist at a state DNR and the decade before working for a non-governmental scientific organization. The story usually involves black helicopters flying at night who drop coyotes and venomous snakes with little parachutes - because....well, who knows.
Coyotes flourish where we have wiped out the predators that were native. In many eastern states, the earliest laws in the 1600's were predator eradication laws that specified bounties for mountain lions and wolves. These large predators had large ranges and it was easy to eradicate them in a few decades with the incentive of bounties. With no real predators, we have overpopulation of deer (athough the habitat is also more favorable for deer today too).
I was always impressed that every person who somehow managed to catch a fish was smarter than every fisheries biologist and every person who saw a wild animal knew more about wildlife than every wildlife biologist.
I'm inclined to agree with you regarding coyotes; they're found in most major cities now and that's not because they were introduced by state/federal agencies. Lots of food opportunities and no real natural threats to keep them in check.
I know for a fact that large predators have been reintroduced into areas though; in this case I'm talking about Mountain Lions and the state of NE. I was born and raised in NE. I spent a good deal of time hunting/trapping/fishing (did quite a lot of coyote hunting too). Despite the official state word otherwise, we knew there were a few Mountain Lions in the area. I never saw one live, but it wasn't uncommon to see tracks near water sources. Those tracks were too large for a bobcat. Twice I've seen what remains of a calf carcass up in a tree.
There were a lot of coyotes in the area, and I've seen a good number of coyote kills, but never one where the carcass had been dragged 12 feet up a tree.
Sometime after I had moved to NJ the state's story blew up (I think it was in the mid 1990's).
One wintery day a homeowner (in the small town - directly across the street from the elementary school) opened his garage door to get his snow blower out. Inside the garage was a grown Mountain Lion. Long story shortened - the local cops ended up shooting/killing the Lion. Being a very small town in a state without Mountain Lions, this made the news and it wasn't long before the state officials were asked how a state that hadn't had Mountain Lions in nearly 100 years could have a Mountain Lion in some guy's garage in a small town in the center of a large state.
The state was forced to admit that it had been slowly reintroducing Mountain Lions for quite a number of years - and hadn't told the public about the effort.
It wasn't just a matter of not telling people though; the state routinely (and falsely, it turned out) denied the possibility of there being Mountain Lions in NE. Those who hunted frequently knew better though. Farmers and Ranchers knew better too.
To be fair I had not assumed that the state reintroduced Mountain Lions. I figured a few Lions hadn't looked at a map and/or didn't know they weren't supposed to move into the state of NE - or they hadn't bothered to notify the state that they had taken up residence in NE. As it turned out, I was wrong: the state did reintroduce Lions and was aware of the fact that there were Mountain Lions in the state of NE. I don't know if the Lions ever bothered reading a map though.
The scuttlebutt in NJ is that the state reintroduced coyotes that are a mix between eastern coyotes and some Canadian Wolf. There seems to be a bit of support for the coyote/wolf theory, but I'm not completely sold on that one. The coyotes (in NJ) do seem to be a bit larger than the coyotes I recall in NE - but I haven't seen many NJ coyotes so the jury is still out.