The objects we have detected look like classical GR black holes, yes.
The problem is that, theoretically, there are other possible objects that look like classical GR black holes from the outside for a very, very long time, but still aren't classical GR black holes. We have no direct way of telling from observation whether the objects we have detected really are classical GR black holes, or whether they are one of the other possibilities.
What evidence would you require to confirm that they exist?