I thought that could be the case, but to have a redile with no date the mechanism would have to be modified.... and it seems that it was always a no date movement.
I also have a Jlc Chronometre calibre 906. The question is that my watch is a no date..... the mechanism is the proper calibre 906 and hasnt been modified do the no date face. The dile looks to be with the right wear for a 1970's watch, the only question in my head is that it only has Swiss Made on