That is correct. They won’t hand you the letter and walk away. (otherwise, people could just get mail delivered for free in the same city, by switching the destination and sender adresses) So make sure you have the exact change/cost of the stamp on hand. Your letter will be held hostage until the due amount is cleared.
People have tried to get slick, and send mail out of city as well, for free. Say the senders address is out of city. (example, letter is in Dallas. Destination is in Dallas. But the sender address is in Austin) Post office will not return to sender. Post office carrier will actually go to the destination address, and demand the money from that person. lol Post Office assumes they actually tried to pull a fast one. How else did the letter even get to Dallas without a stamp? They figure the destination, is actually the sender, trying to have it “returned” to the fake sender…who is actually the true destination.
letter in same city as sender address = carrier goes to sender, demands money for stamp.
letter in same city as destination address = carrier goes to destination, demands money for stamp.
Either way, they hold that letter until the stamp cost is paid.