This is possibly the most important thread on Permies - nay, on the Internet. Thank you for raising this urgent topic.
I have thought an embarrassing admirable amount about this already, and I think that basically you are all right. The basis for my argument is primarily linguistic/etymological. We can start with the word "pie" in its various cultural/historical applications - standing-crust pork pies, pot pies (with only a top crust), shepherd's pie/fish pie with their potato crusts, Cornish pasties, and so on.
Another word for pie? Tart. Thence, we can consider cognate terms in other languages, like the Spanish torta. A torta can be a cake, but it can also refer to a sandwich. So a sandwich, I argue sincerely, is a pie. It has a crust on top and bottom and contents within, so hardly a stretch. And, of course, a "little sandwich" (or "little cake") in Spanish is a tortilla. Clearly, tacos are pies, as are burritos, enchiladas, quesadillas, etc. Now for Italian. Tortellini are also little pies (makes sense) even though they are boiled and not baked. So that means many Asian filled dumplings and buns qualify, as well.
Pastel is a Spanish word meaning, approximately, "pastry"; this word was applied to the Puerto Rican dish consisting of a mash of starchy roots stuffed with meat and then boiled in a banana leaf. Pie. From there, tamales are clearly pies. Pastelillos are little pies, and so clearly are empanadas and rellenos de papa.
Pizzas are pies. Pita is a pie, and a pie-forming word element (like spanakopita, spinach pie). Stromboli, calzone. I would argue that lasagne al forno is a pie.
We haven't even breached sweets. Mochi are pies, onigiri are pies. Pumpkin pies, pecan pies, chocolate pies, cream pies, Bakewell tart, spotted dick, roly-poly pudding, Jelly rolls, filled doughnuts, baklava, pasteis de nata, cheesecake - the list is nearly endless.
The connecting element between all of these is the human practice of covering, holding, or encapsulating a non-starch food substance, often of a variety that is difficult to hold, within a starch food substance, frequently (but not always) permitting it to be stored, transported, held, or eaten more neatly or easily. Thumbprint cookies. Sausage rolls. Pot stickers. Toad-in-the-hole. Obleas. Sushi. Hot dogs on a bun. Pain au chocolat. PB&J. Chili cheese fries?
If you have been touched by this expansive vision of pie, you will be pleased to know that the membership fee for my pie cult is currently reduced to a mere 3.14% of your gross income.
