But they are (unwittingly) using the other DB as a source. The data they're scraping turns out not to have been created by the supermarkets in question but sourced from a third party database and published under license on the supermarket websites.
How about we try out a reductio ad absurdam: I'm going to start a startup. Our business model is to license the information on customers' websites, and then license it back to them in turn. This then means that anyone who uses our services in the UK can sue for copyright on lists of facts obtained by screen scrapers, as they've been through our database copyright washer. Think flight prices, hotels, cars, anything.
Is that a viable business model? If not, why not?
Someone is creating a phone book as a service to companies.
Elsewhere, these companies are publishing their phone numbers to get more customers.
Then the phone book creators demand license fees anywhere these phone numbers appear in lists.
It's very dubious "database rights" come into play at all.