Hi Art,
I don't know whether or not there is an authoritative account of this interesting part of horological history, but I have come away with the clear impression, having digested a variety of sources, that there was some sort of dispute.
It is, as far as I can gather, unquestionably the case that Buren patented their design in 1954, while Universal Geneve applied for their patent in May of 1955. During that early period, UG was forced to label their movements as "patent pending", and, as a result of the dispute, were not able to recorded the actual patent until May 15, 1958. There is no doubt that there was some sort of "legal trouble" encountered by UG, but I admit that I cannot say with certainty that they paid royalties to Buren. I suspect that they did, but quite probably only until their patent was granted.
Best regards,
Tony