Let's assume Theory B is correct, and searching for a faucet and then stopping can be treated as having bought a faucet. That tells the advertiser that the user buys faucets, and that's exactly the right person to advertise to. I'd bet that in a large number of cases someone who buys a faucet is likely to buy another faucet in the near future - faucets are something that you buy when you're doing up a house, or you've moved house, etc.

Advertising to someone who you have reason to believe is going to buy your product is much more effective than advertising to an unknown person.