I used to work for a very big car lease company .
end of lease cars got inspected,any dents,damage,missing wheel trims ,gaps in service history got billed to the leaser ,
any car that was rough,had mechanical issues,missing history ,bad damage etc got sent to the pound ,fuel removed,tyres with good tread put on retail cars,then sent to auction.
any cars that where in good nick got picked for retail,prepared, minor dents etc (PDR) done,full valet, stone chips touched up dealer number plates and stickers etc etc
if a retail car did not sell in 6 weeks ,then it got sent to auction as old stock.
so a valeted car with flat battery may be just that, a retail car that went old stock because the sales team never showed it anyone because they where lazy and had plenty of other stock without finding a jump starter pack.
part exchanges just got sent to auction (or purchased by savvy staff
if any good)
auctions are ok,IF you know what to look for ,but you can still end up with egg on your face,
private sales let you test drive ,check everything etc (mostly) but you can still get caught out (people sell cars for a reason)
retail sales, you tend to have some come back ,IF your purchase turns out to be yellow and citrus