André and I saw some while hiking in Chiricahua National Monument during our trip in 2002. We were on a longish hike (very few people on the trail) and suddenly saw what looked like monkeys run off in the distance. Now I know that monkeys do not usually live in Arizona, but I had no idea what else they could be, so we had to ask at the ranger station after we returned from the hike. The ranger told us that we had probably seen some coati mundi (or white-nosed coati, ring-tailed coati), which is rare because they are pretty shy.
The other time I thought I’d seen African animals in the USA during that trip turned out to be neither a mirage nor a species unknown to me: I saw some oryx antelopes, which I had previously encountered on a trip to Kenya. It turned out that someone actually set some oryx antelopes free in the US in order to hunt them. Having no enemies, the population apparently grew quite a bit.