Several comments on this interesting thread.

(1) I have frequently found that if I search on consecutive days for a particular routing, United will (I assume) sense that I am interested in it, and the price will rise even though the same fare classes are still available.
(2) I have frequently found Google to produce fares that are both lower and higher than what I could find on the United site. No rhyme or reason to it.
(3) I have also found that when finding a lower fare on Google, and then booking through United, everything goes swimmingly and United confirms the lower fare, right up until the final page, when the total to pay suddenly and inexplicably rises, something by as much as 300%. This makes me think that the Google lower fares are sometimes phantom fares that no longer exist.