This is about falling for marketing sucker terms such as "concierge". Face it, you're talking to a reservations agent with a bit more experience and authority than the run-of-the-mill. That's great if you need a room with a specific view or a special blankie or whatever.
But, OP isn't a guest at the hotel, this is a financial transaction and the SPG agent isn't going to have a clue what's doable and what it costs at the specific location.
In this situation, I would either call my local FTD florist and make the arrangements or I would call the real concierge at the property directly and get it done after figuring out who to pay for the flowers, provide a hefty tip to make sure it happens and not have the whole thing appear on the wife's bill.