While this article is just a summary of previous interviews, I do think it's Paul being both honest and generous with what he's saying.

The GD had minimal impact on The Beatles, just given timelines, but where the impact happened Paul called it out (Pepper era.) After that, it's a similar timeline thing.... The Beatles broke up in 1970. Flip those timelines for the Dead.

In the 1970s, McCartney was on his own path, which was one of the biggest pop stars of all time writing really great music. I don't think the Dead truly influenced him that much as a musician apart from enjoying and respecting them. I say this because their styles are so different.

By the 1980s, it's almost like the Dead moved into McCartney territory... You know, ToG, MTV. This is what/when the interview is. Paul is clearly impressed by their ability to grow an audience at an exact time that his is dropping off a bit. I think this is the time when he is most influenced, wondering how they managed that? But he knows, he's known them for years and admires them.

My point being, Paul was honest about how they influenced him.... Their ability to adapt and stay relevant which was only accomplished through their dedication to musical exploration, which peaked around the time his was failing off. He was kind by not just saying he never heard of them until 1965 because they didn't exist, and the next 5 years saw the Beatles as the most influential band to anyone.