I had noticed the fact myself a few years ago, and although I tried to find a reasonable explanation, I haven't been able yet...
Danny Shaughnessy wrote in his wonderful book Evergreen, "In 1957... Red Auerbach and (owner) Walter Brown contracted New England Flag and Banner Company of Watertown to stitch the first championship banner. It was made of cotton bunting and measured eight feet by twelve feet". When the Celtics won another championship in 1974, new owner of New England Flag Joe Studley found out that the banner blueprint was lost. The plans were eventually found. In the eighties every banner (now made of nylon) cost 475 $ each, a fact that must have made some thieves hungry, since some of the originals were stolen. Then-General Manager Jan Volk said "That's a terrible feeling when you look up and say, 'Oh, my gosh, 1957 is missing'".
So, in all this brouhaha of changes, blueprints lost and thieves, it is quite probable that one day somebody decided to stitch the new banners changing the NBA logo and making it white with the two green half circles on the top and on the bottom.
I hope this helps...