Without knowing type of controller, see a schematic of circuit board it is not possible to KNOW, but for the sake of discussion, IMO...
If someone designed a sprinkler circuit board in such a way that the rain sensor can override OFF, I think they missed a few classes in college, or had someone in marketing/sales supply the requirements. You can almost imagine a sales person saying wouldnt it be cool if the sprinklers knew the grass was dry and overrides off ...
IMO, the only way the sprinklers could come on is if someone manually turned then on in valve box OR you have a defective circuit board...
would love to hear what you find...
good luck.