I have run speakers that most would be considered to be outclassed by my electronics for a couple of decades. Your interest in an integrated is appropriate and will get the most out of your speakers. Should you ever decide to upgrade, then you know you can upgrade your speakers and have an amp to support them.
As far as your salesman saying “The salesman at my local audio store said amp technology has not changed since the mid 80’s” The is categorically misleading and patently false. The performance levels since the 80’s has changed profoundly. This is the kind of statement to come from a salesman where I would politely as for the manager and see if the manager actually knows anything about audio.