Oyster PAYG/Contactless are emphatically not tickets, given they can't be used in conjunction with a paper ticket to/from a location outwith the PAYG area without touching in/out as appropriate. Rather, they're more akin to an authority to travel (and Contactless muddies the waters further given you're not actually charged until the end of the day, or a few days later.)You stated they advertised “You may use your ticket on London Underground services at no extra cost"”
Oyster/PAYG is your ticket in this situation. It shouldn’t matter. Shouldn’t.
LU's internal information regarding ticket acceptance makes it clear that it only applies to ordinary tickets and staff passes (where appropriate) and that customers using Contactless/Oyster PAYG will be charged the appropriate fare for the journey actually made, given there's no simple way to tell the Contactless/Oyster back office about the ticket acceptance.
Unfortunately, most TOCs don't understand the distinction between the two, so don't include this crucial information in their engineering work notices. In the same vein, they generally don't seek ticket acceptance on London Buses where appropriate either.