First, is there another record of that period of time we can turn to?
Second, does it matter?
Fact is, millions of Christians accept it as truth as the dogma of there faith. We can not disarm criticism against us as Jews if we can not at least accept their perspective (if not their conclusion).
When conclusions of deicide are based on ignorance of their own religion (and there are many "Christian biblical" cites absolving the perpetrators of the crucifixion- the least of which was my own analysis) we must have a dialogue based on somebody's reality - saying it never happened will hardly resolve any abrasiveness.