Several years back, I read on a Piaget forum that Piaget used to provide movements to VC. This was confirmed (by Alex/VC/THL...I forget) to not be accurate.
I saw this $20 coin watch being offered at the Christie's auction in HK later this month. What caught my eye was in the second line of the description, "signed Piaget".
VACHERON CONSTANTIN. AN 18K GOLD TWENTY DOLLAR COIN WRISTWATCH
SIGNED PIAGET, REF. 6510, CIRCA 1975
I saw that several coin watches, from various brands, were being offered at this particular auction...including from Piaget. So I am guessing that it was a copy/past mistake. It just happened to ring a bell in my head about something I read years ago.