Almost everything of interest essentially happens in our backyard because that's the place we can see with the most detail. It's a little like looking out at the Universe and coming to the conclusion that we're in the middle of it because the "edges" are all around us.
Even if this was rare and there happened to be tonnes of very old stars only close to us, this could again be coincidental, especially if intelligent life is more common than we currently know.
This is precisely true, only very small stars last very long, and small stars are very dim. All the old stars that we see must be very close. The bright stars that we see that are far away only live for a few million years.
Even if this was rare and there happened to be tonnes of very old stars only close to us, this could again be coincidental, especially if intelligent life is more common than we currently know.