Yeah I know it's not a strong case but they certainly already had the information and, had they approved all 3 cards on the first day, they likely would not have pulled the report 3 times.
I probably won't pursue this at all because I knew this was a possibility. I'm just surprised because I've been doing this often for over 2 years and never had more than one pull if all the apps were for a personal card and no reconsideration was required.
On a side note, is it reasonable for a credit card company to wait 3 weeks to pull your credit before considering your application? I don't think so. That's essentially what they did here. They approved the first card immediately, then the second card about a week later, and the third card about 10 days after that. If they "began" to consider all three on day one, then the first pull was sufficient. If they didn't even consider cards two and three until a week or two later, then I don't see what they gained by pulling the same report again.