US: Immigration officer demanded I leave the country after 2 months (when VWP gives me 3 months)

I had a very traumatic experience recently while trying to enter the US. I was almost denied entry for having a "story that was too vague" according to the immigration officer.

I lived in the US and had an H1B visa before, but after quitting my job I left the country and came back a month later as a tourist under the VWP program (I'm from EU, btw). Anyhow, I never overstayed, worked as a tourist, had any problems whatsoever and/or committed any crimes. In short, I've always been a law-abiding visitor, both when here with an H1B visa and as a tourist.

This time, I again entered as a tourist (note that this was my 2nd tourist visit; there was an almost two-month gap between the first one mentioned above and this one). The immigration officer said my "story" didn't check out and I had to undergo the secondary inspection. The 2nd guy was very unpleasant and hostile, and basically treated me like I was some sort of criminal (I get it, that's his job - not complaining about it). However, when he finally OK-ed my stay, he told me I must leave the country in 2 months. At the same time, the stamp in my passport says I need to leave in 3 months.

What I would like to know is if the immigration officer's verbal demand to leave in 2 months can override the default three-month stay that's tied to the VWP program (which has also been stamped into my passport). Is there even a record of such verbal demands?

Happy to provide additional details if you think that would help. Thanks!