Re-pinning or new strap?

Hi - my Seamaster is about 15 years old and the pins have started falling out of the strap. Have sent it off to be looked at, and the company is 'strongly recommending' I replace the whole bracelet, rather than just replacing all the pins.

Given replacing the strap is about 8x the cost of the pins, I want to sense-check this! They say the bracelet is 'strained' and that new pins might fall out over time also. The strap has never been serviced (I know, I know!) so I guess there could easily be wear on that, as well as the pins.

Obviously it's a bit difficult to be certain, given none of you have seen the watch (and I can't take photos as I've sent it off) - but does their 'recommendation' sound sensible to you?

Thanks for the replies. It was sent off via Ernest Jones in the UK - not sure who they use. They may well be telling me the truth, but it just sounds a bit too close to a heavy upsell...

I recently had a pin come halfway out on my SMP 2265.80 while on a fishing trip. Upon return, I took it to my OB. They inspected it, replaced all pins and tubes that had a foot in the grave and gave my watch a good cleaning. Took them a couple of weeks with it. Total charge: $0