I would agree with the other posts. I bought a 1955 Pontiac back in 1962 that the service department in the dealership had overhauled. I had all kinds of expenses with the car. I had problems with a chirping in the valve train. An oil filter was optional equipment in those days and the engine must have had quite a bit of sludge. I replaced the valve lifters and had the mounting studs in the valve train pulled and cleaned out. Even this didn't completely solve this problem. I had a piston slap in the engine--while not serious does indicate an overhaul that wasn't done correctly. I did install an oil filter on the car.
I had to have new bearings in the transmission--it was a manual shift. I also had to put on new brakes and replace the master cylinder. I learned that there are more things that go wrong with a car than the engine and that a rebuilt or overhauled engine does not guarantee a trouble free car.
Tom McCahill, an automotive writer for Mechanix Illustrated said that in buying a used car that more needed to be considered than the engine. A transmisison that doesn't shift correctly, or a rear axle that howls could be more serious than engine problems, and a bent frame is impossible. He also said that rust and serious body repairs were much more serious than the engine.