[mrweasel]

But why would they store them and why would they have access to the card number?

The credit card processing is normally completely separate from the rest of the POS. The credit card "machine" communicates directly with the credit card processing company and just informs the POS that the transaction was completed.

You would need to break into the encrypted data sent from the credit card terminal to the processing company to get the card number.

Maybe I'm just completely ignorant about how this stuff works.

Target and Home Depot are doing something that they don't need to be doing to process payments, unless skimming is involved.

If skimming is involved: start moving to chip cards and drop the magnetic strip.