Sounds like you're getting sucker information from both dealers.
Unbalanced tires will not damage the wheels.
If you have wheel damage, it's more likely to be from the use of improper clip-on lead weights on an alloy wheel. Or a road hazard.
If the summer tires never went out of balance, then when the first dealer put them on the balancing machine, they COULD have come up needing the same weights as before, hence no change.
Don't overreact.
Unbalanced tires will not damage the wheels.
If you have wheel damage, it's more likely to be from the use of improper clip-on lead weights on an alloy wheel. Or a road hazard.
If the summer tires never went out of balance, then when the first dealer put them on the balancing machine, they COULD have come up needing the same weights as before, hence no change.
Don't overreact.