Authentic Rolex Bracelet?

[vasub]

Over Christmas, my dad (very, very generously) gave me his 1972 Rolex Submariner, originally a graduation gift from his dad. He hadn't worn it in years, so had it refurbished, and gave it to me. The watch is beautiful, but since the bracelet is older, thinner, and doesn't have a lock/clasp, he got another band from a slightly later model Rolex to give to me. More specifically, that bracelet came from his younger brother, my uncle, who got the same gift for graduation in the early 80's. When my uncle received that watch, he swapped it out for a nylon band, and stashed the original bracelet, then lost the watch a few months later in the ocean...

I took the watch into the local Rolex dealer who had facilitated the refurbishment, to have the watch appraised, and to have the bracelets swapped out. I was told today that they could not use the bracelet that I provided, because it was "not of Rolex manufacture". The sales rep noted that the clasp had some rust, and that the links were kinking here and there. They were very friendly, and while it's not that I don't trust them, as they seem to know what they were talking about, I thought I'd get some verification/suggestions on tells from the internet before I buy a new bracelet.

I've attached a few pics.