Tobin, I understand your point. Like I said I will pay a premium to a LDS, within some boundaries.
Point is I expect you to keep those prices same for all customers, if market conditions are the same.
I do not know how business in US is done, but here we have customer protection laws which say that if I bought item X at price Y, they can not sell you item X at price Y+Z, unless there has being changes in their operating expenses. All customers must be treated the same, whether they've done price matching search or not.
Customer can ask for a discount, but price matching is not discount, it's trying to make a sale in any way possible. Like
@stuartv said, if I found that you sold me same item for higher price than you did to him, do not blame me if I choose to buy online next time.