Christmas is just the celebration of Jesus's birth, not his actual birthday.
The church knows this and always have... they where the ones that moved Christmas to coincide with some pagan holiday that was already in existance.
It's not a hidden conspiracy... and it doesn't prove the non-existance of either Jesus or God. It's just a day chosen to celebrate an event. Think of it like Earth Day, except more important.
Earth wasn't born on Earth Day, it's just the day we've choosen to celebrate it.