Hi raczar,
I agree, the lovely tree in question is a
Loquat (Rhaphiolepis bibas). In our former neighborhood, our backyard neighbor planted them all along the perimeter of the property between our yard and hers. They were so beautiful when in bloom in spring but they did pop up everywhere in the flower beds and in the lawn. Gray Catbirds and Squirrels love the fruit. I worked with a lady years ago who used to make jam from them but what a tedious job that must be since the fruits are small and mostly the large pit in the center. I think I came across a couple of seedlings in our new backyard last week but haven't had a chance to thoroughly investigate yet. If they are loquat I will dig them up and put them in a container for my sister and brother in law who'd like to have one.