I wonder whether, when a US lawful permanent resident enters the US via SFO's global entry lane, they have to speak to any US Customs and Border Protection (CBP) officers or whether the entry process is fully automated.
Adding to "mlc"s comment: I have entered the US (not SFO) about 4-5 times this year and the process is entirely unpredictable. Sometimes Global Entry is entirely off, sometimes it wants passport scanning, sometimes it wants face recognition. Functionality and availability of kiosks is spotty. Sometimes you get waved through, sometimes they look at your passport, and sometimes you get engaged in a conversation.
My daughter tried even though her GE had expired AND there was a name mismatch between her passport and the booking, and they still just waved her through with the comment "it's fine, the machines are acting up today".
At my Global Entry interview, the interviewing officer made it abundantly clear that Global Entry clearance is not a guarantee of any special treatment. They reserve the right to interview, search bags, etc. should they see fit.
What do I do if the Global Entry kiosk issues me a receipt marked with an "X"?
If the kiosk receipt has an "X" printed on it, you must report to a CBP officer at the nearest staffed CBP passport control booth. You do not have to get back in line. The CBP officer at the passport control booth will review your documents, determine the reason for the "X" and either release you from there or refer you to "secondary" for additional processing.
A US LPR returning to the US is exactly the same as a US citizen returning except the LPR will scan their I-551 (green card) in the machine rather than their foreign passport.
Whether or not anyone returning via Global Entry will need to speak to someone seems pretty random. The most common conversation I've personally had is asking about the food items I'm bringing back. It has never resulted in any additional screening required, but I've also never brought back anything that would be considered unusual.