I just coming back from filling up at Sam's (not top tier) the 05 X3...not only do I take the gas cap off first but I untangle the pump hose most times. Im sure I've experienced what you describe but it's far from memory. Yes, I would say it's the pump itself...gas may come out super fast and therefore the "off" click.
My concern:
I've read that if the engine stumbles right after filling up completely the gas tank...that's an indication/symptom that it's time to replace the gas tank pump?
This has happened to the x in the more recent past.

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