Eh, I've never argued that he didn't exist, for more or less the same reasons that you do. No matter how critical or pro-Rome/anti-Xeno Roman historians were (well, a good chunk of them, I'd like to except Polybius from that list on the grounds that he realized Rome subjugated Carthage and that they were in fact, not barbarians), they were usually quite accurate. The thing is though, he never agrees to Christ having divine powers, only that he claimed to them, caused a revolt in Judea, and possibly caused his followers to burn Rome (though not purposefully, and indeed that may have been a manufactured lie).
Anyway, don't mean to get off-topic, just saying it doesn't prove Jesus was divine (though you never claimed it did, I feel it necessary to point that out).