To the extent such a rift did exist, I wonder how much of it may have had to do with Payton tying to work the deal with Miami where he and Brady would have went there? That would have been a breach of his contract to talk to Miami without permission and may have lead to some issues between Payton and Loomis in the last couple years.
Still, I think if there was a rift that was that bad, Payton would have demanded a trade instead of retiring for a year. After all, he had to be traded anyway due to being under contract when he retired.
So, if there was a rift, I don't think that was a major reason for him retiring. I'll take Payton at his word that he was burned out and needed a break as the main reason. But, given his history of looking for other jobs and the number of times his mentor Bill Parcells moved, I think he was just looking for a new place to work because he felt he had stayed here too long and wanted to get a fresh start someplace else.