Your first impression was correct- the choice of the date Jesus was "born" was deliberate. Right at the end of the pagan celebration and three days after the winter solstice.
American Christmas, however, is an invention of Madison Ave. ad executives (as was jolly old Saint Nick- Santa Claus), as a way to sell more during the darker season of the year. Capitalism, the American version, at least, will always find a way to sell more products and make more profit and if a revered religious figure is used then the money still means more than hope and love. In this nation, the dollar is the almighty...