Gnerally a fault needs too be present for two drive cycles before a CEL is set, first drive cycle sets a pending code and then on the second drive cyccle if the fault still exists a CEL would be set.
Never rule out fuel pressure until you've actually seen what the pressure is when the car is stalling, a sudden fuel pressure drop would not cause the car to "sputter" it'll just stall and would not set a CEL
Ive driven around with fuel pressure gauge hooked up to the car, gauge was at 43 psi after a stall out. That being said I have pretty much ruled out fuel and am focused on electrical/ignition.