The filter does indeed have a check valve that should maintain pressure for quite some time after the engine is shut off.
To see if this is the problem, just turn the key on for about 5 seconds before trying to start, that should build up pressure.
Another possibility is an injector allowing the fuel to pass without being triggered.
Does it smoke a bunch when first started ?
Does the oil look diluted with gasoline ?

Here is a diagram of the fuel system :