Lots of things require a full payment upfront, although deposits are more common. It's certainly not an unheard of policy. I don't think you are going to be left in the lurch either way. Even though there is no written contract there is still a verbal contract, and no court (if it were to come to that) is going to believe that you verbally agreed to purchase the bike regardless of condition. So if it were to come damaged, the store is going to refund you your money. Put it on the credit card as well and you get a little more control back.
Also in reverse if the store were laying out the initial cash and only required a deposit and the bike came damaged and you walked, they would then ship it back to Specialized and get their money back. At no point in the retail model is anyone ever agreeing to purchase damaged new equipment unless it's a discount. There doesn't need to be a written contract to explain that.