Hi Alexander,
No, you can’t. The National Rail fares database has existed since at least privatisation, maybe before. The PAYG fares database was created to run the original Oyster system in the early 2000s after TfL gave up waiting for the government to specify a smartcard solution. [It’s Cubic by the way, not Cubitt, who run TfL’s revenue contract] As far as charging people for PAYG the master database is TfLs. National Rail wanted to show PAYG fares on National Rail Enquiries so they set up psuedo fare types so they could handle that. I don’t know why they didn’t access the live fares database like my site does, but I’m sure there were reasons. Because there is no link between the databases it is a manualish job to enter the fares onto National Rail. Mistakes often creep in via this process. The bottom line is that all PAYG fares are charged according to TfL/Cubic, be they tube, dlr, NR, cable car, boats, buses, trams etc etc etc.