IMHO, I think that myth was put out there as a ploy to divert the attention away from Jesus because the masses will believe falsehoods easily and blame churches instead of the devil who lies. How many families do you know who refuse to participate in Christmas celebrations because they have been told it's really a pagan holiday so they refuse to even look to the truth of Jesus. Candy canes indicate a shepherds hook as well as an upside down J for Jesus and the red holly berry represents the blood of Jesus and then you got the bells that were a part of the Jewish priests' garb. There are symbols abounding that have been lost in the secular world and mocked by our very own Christian brothers and sisters.
For what it's worth it seems more believable to me to figure that Christmas was put in December to draw attention away from Yule logs and winter solstice celebrations, than arguments about candy canes being a J for Jesus. To me that makes no more sense than the claim that we exchange Easter eggs because the stone in front of the tomb was shaped like an egg, it seems like the kind of story that might persuade a child but then leaves them vulnerable to more reasoned arguments about pagan fertility goddesses.
Ultimately the exact date Jesus was born isn't relevant - he never told us to commemorate the date he was born. Anyone feeling so inclined could probably dredge history books and identify when the census called by Caesar Augustus actually took place (from Luke 2), figure how long it would have taken to travel from Galilee to Bethlehem, and from there gauge roughly when Jesus was actually born. It may be possible to cross-reference Matt 2:16 to determine when such a substantial execution of children took place, to verify the approximate date. Either way the fact that Christ came is far more important than the exact date he was born.
Of course the flip side is that Jesus never told us not to commemorate his birth either. Whether December 25 actually marks the birth of Christ, was hijacked based on Saturnalia, Yuletide, the winter solstice etc, or was just made up because it was as good a guess as any other, doesn't make it obligatory to either commemorate the day or refrain from commemorating the day.