I have never tried to put 16 inch wheels on a vehicle that was originally equipped with 17 inch wheels - except by mistake!
When I did this, I realized my mistake when the wheels would not fit over the brake calipers. So, I would tend to agree with the tire stores.
On the other hand, different style wheels will fit differently also. Some are deeper than others, besides being different in diameter alone. So it may be possible to find a 16 inch wheel that will work.
In any case, I highly recommend that when you go to purchase the wheels, get the seller to actually try one on both the front and on the rear before buying them. The front wheels and rear wheels usually have different clearances. If you are buying them used, make sure you have the option of returning them and get a full refund if they will not fit. Make sure they will fit over the brakes and backing plates. I have even seen people that have bought wheels only to find out that they interfere with steering knuckle, tie rod, strut, or spring clearance. Many NEW tire and wheel retailers will not have a problem with "test fitting" for you if they think you will purchase them if they fit.
If the tire stores are telling you that they will not clear the rotors. they are probably correct, but you still have the option that we use here in Missouri..."Show Me"!