Yes, the origins of the holidays are true. However, I do not think those holidays would be the dominant, work-force-holiday-dominating forces that they are if it weren't for the Christian influence. I maintain that the relationship of those holidays to Christianity is the reason they are dominant holidays now.

After all, without inter-Christianity-bickering, the Pilgrims might never have come over here, and Native American religions might be the dominant on the continent. I'm pretty sure that they don't have Christmas- and Easter-esque holidays at the center of their religions.