Bring it to the shop, but you ask to witness them spin all the tires in front of you on their balancer. If there are any bent rims, you'll see it immediately as they are spinning.
If they are a good tire shop, you'll also see the readout on the balancer and if they are balanced or not.
The other thing I've seen in the past are tires that have belt shifting issues right from the get go, brand new. You should also be able to see this when the tires are spinning (hop and/or wobble on the tires, and not a wobble on the rim)
If you are not confident in the first shop, eat it and go to another shop and pay to have them checked, but, you witness it.
Also, did you check the date code on those new tires as well? Sometimes those amazon deals are done to get rid of old dead stock that's been sitting around for a while. If they were stored incorrectly over a long period, or possibly abused whilst stored and/or in transit, it has potential to damage the tires and/or disturb their structural integrity.
I don't disagree that sometimes in these trying economic times one needs to hunt for a good deal, I do it a lot. However, when it comes to certain things, a great deal may be too good to be true, and with "new tires" from Amazon, one needs to be aware of what that deal may actually be stemming from.