?? How do you have Global Entry without a US passport? I thought it was limited to US passport holders. Do you use the GE kiosks when you arrive in the US after an international flight with a non-US passport?

Different airports and checkpoints are configured differently. Did the TSO who looked at your ID scan it? If you are Pre-cleared (not the same as Pre-eligible), the scanner will give 3 beeps. There's no manual way for the TSO to determine from your boarding pass if you are Pre-cleared for a particular flight.

Even if you are using a TrustedTraveler ID (GE, NEXUS, etc), that only means you are eligible to be in a Pre-Check entry lane (which may be the same as the elite lane). You will not be Pre-cleared for expedited screening unless your boarding class scans OK.

Did you keep your shoes on, laptop/LGAs in your bags? Generally the TSOs manning the xray will advise you of this if you are actually in a post-TDC Pre-check lane.

At one airport I use, there is now a Pre-checker at the beginning of the elite/Pre-check shared line leading to the TDC. Some folks (non-elites) were presenting as Pre-check candidates, thinking it was a way to get into a shorter (elite) line to the TDC, since you don't have to present a Pre-check ID of any sort, you just get your BP scanned (and some Pre-check eligible folks still fail).

Now they've gotten wise to that. At the airport I'm referring to, there are two people checking you before you can enter the elite/Pre shared lane leading to the TDC - you have to either clear the TSO scanning your BP for 3 beeps or the airline employee checking your BP for elite status.