"In addition, I almost missed my flight in Amsterdam back to the US last year when I was not able to readily show them verification of how and when I entered Europe. I would’ve assumed that my passport stamp would have been sufficient enough for that, however, that was not the case.
Q: Who/what found the passport stamp insufficient evidence?"
A: AMS is typically my arrival/departure point in Europe. Starting in 2016, AMS initiated a Pre-Departure Center for required security screening in on select/most flights to the US. For me, predominately a Delta flyer, after passing through security, you head to gate D1 for another round of security. This is the moment where the security personnel has always required that I show documentation of my inbound flight (IF I did not book a round trip). This security appears to be a joint effort of AMS security personnel and Delta.
The only other airport I was asked to show my arrival information when passing through security on my way back to the US was in Dublin, Ireland, which has the US Pre-Clearance process in place. I have to assume that was a one off, as I have never been asked to provide that information prior to and since then. However, due to the fact that I have had to have my one-way itinerary available at the Delta PDC EVERYTIME while passing through, I keep both itineraries at the ready and recommend other travelers do the same, especially passing through AMS.
I do NOT bother doing this when I book round trip, only when booking two separate one way itineraries.