Rolex wants me to change my bracelet on my Pepsi

[Roly25]

So I went to the RSC in Manhattan the other day to get my bracelet adjusted on my 16710 from 1996. I wanted a permanent link removed from the 6 o'clock side, which they did no problem.

However, while there they told me I should change out the bracelet since the one I have has a lot of stretch. They were telling me it could fall off my wrist. Now on my way out I stopped by two Rolex ADs and both service guys told me not to worry about it. That there are vintage Rolexes from the 60's, 70s, etc where people still wear the old bracelets.

I love the watch, but I just picked it up. I don't want to drop whats about 1/4 of the purchase price on a bracelet right about now. Does anyone on here have any experience with bracelet stretch? Has it caused any issues with your watch? I might as well buy a nice leather or put it on a NATO if it is an issue.