Why is a product's discount greater than what is set in the Max discount field on the product?

Max discount percentage still appears in a campaign, you may have forgotten to remove it when setting up the campaign.

If a product which you have set a Max discount percentage on in Products (PIM)>Products still shows up in a campaign it could be because you haven't removed the product when you set up your campaign. A warning will appear indicating that a product/products exceeds the set percentage of the campaign. If no action is taken the product still will appear in your campaign. You can easily review or remove product/products from selection or adjust specific product to the correct max percentage in the Discount(%) column.