Peregrines will hunt ground critters in places like the arctic where they can be more numerous than birds in some places. Among the anatum (our subspecies) there are rare reports of mammal prey remains being found (mostly bats). Note, that if you find remains, then they really haven't eaten it - killed it yes, eaten it no. As for a peregrine hunting mice, if it was, it wasn't really looking for food, entertainment or practice maybe - mice just aren't worth the effort, its like eating tic-tacs ... imagine how many tic-tacs an olympic triathlete would need to consume at the olympic games and you get the idea of how worthwhile hunting mice is for a peregrine.
Now kestrels, they are wicked mouse hunters, so too are some of the hawks. Last spring when we had standing water on most agricultural fields, the hawks - Red-tails, Swainsons, Sharp-shinned & Broad-winged - were stacked up on the telephone poles and on higher dry spots waiting for the mice to be driven out of the field by the rising water - it was worth the effort even of the bigger hawks because of the sheer numbers of mice available. But they hunt ground mammals as part of their regular diet, so just a case of taking advantage of an opportunity. Peregrines are bird-hunters and are designed for it, so hunting close to the ground is not always as safe for them as for the mammal-hunting raptors, different hunting mechanics.
So could have been a bored peregrine, but seems unlikely as they are trying to put on weight and are starting to get into migration-mode. Could have been a kestrel or even a merlin (they are better closer to the ground than peregrines) hunting - same flight profile are often misidentified when spotted from moving vehicles (I've given myself whiplash more than a few times over the years and still can't confirm the ID on the move!!!). Or it could have been a sharp-shinned, they are about peregrine size or even a coopers which is bigger than a sharpie.
But then, I wasn't there and didn't see what Eli saw ... could it have been hunting smaller birds Eli? I know fall migration has begun among the passerines here .... blackbirds? flickers? something like that maybe?