Sociologically: there is a surprisingly large contingent of people who believe that if a company makes a claim, it's the God's honest Truth. The OP may not necessarily fall into this camp.

Technically: if the browsers were somehow phoning home, even if the data were highly fuzzed, I'm sure there would be guys like tpatcek who would manage to detail, if not the content of the tracking, at least the amount of data sent and the targets. I don't recall there being such a scandal in recent memory.