FD
This would further be supported by the fact that changing the tanks as attempted made no difference.
What I've read happens occassionally is this:
Assume somebody runs a tank dry (or takes off with an empty tank and that tank is selected; yes, it's been done and I've seen the result) and the engine stops. The pilot does what he's been taught; pump on, switch tanks. You then have to wait some 10-20 secs (there is an FAA certification requirement on this max time in a SEP but it is hardly going to have been checked recently in a typical 30 year old plane) before the fuel from the other tank works its way through the system, and this feel like ages when you are going down at some 1500fpm. So people assume that wasn't the problem, and switch back to the original (empty) tank. Shortly afterwards, the fuel does reach the engine, which briefly restarts, but then stops because the tank now selected is the empty one. Which leads the pilot to assume it cannot be a problem with a particular tank....