The answer is "it depends". If you want mid-80's water when the nights are 40's-50's and the days are 60's then the dealers aren't too far off. I suspect a 4x12 is a custom panel and may be expensive. Standard sizes are: 4x10, 2x20 and 4x20. 4 4x12's are about like 2 4x20's and 1 4x10 (192 sq feet vs 200 sq feet).

But if you are talking warming the water when the air is in the 70's and 80's, 2 4x20's will easily be enough, and 1 4x20 plus 1 4x10 should be enough.

The standard formulas for how many panels you need 'WAY overstate most circumstances. It doesn't hurt, but you may spend a lot of money you don't need to spend. A good installation should allow for more panels to be added easily. It's all just PVC so it's easy to plan for additional panels to be plumbed in.

But given your description of March days, with implicit wish to swim, I don't think the dealer is steering you wrong on sizing.