Found a pretty cool cover of 9 imitating Spider-Man. Y'know, I wonder what The Doctor thinks of Spider-Man, time to check the TARDIS wiki!
So just reading here, it seems that both The Doctor and Spider-Man have encountered one another before, maybe not literally but enough for the purposes of this post.
Some lines from the wiki:
"The Seventh Doctor once stated "With great power comes great responsibility", a quote he thought came from Marvel Comics."
"A glimpse of Spider-Man fighting Doctor Octopus was visible when Esterath explained to the Eighth Doctor about the Omniversal Spectrum."
"The Tenth Doctor noted that the uncle of a "friend" of his once claimed that "with great power comes great responsibility.""
"During an attack on the Fifth Doctor's TARDIS, a Spider-Man cartoon show was playing on the scanner screen, shortly before the screen's destruction."
"Grant told the Twelfth Doctor the origin story of Spider-Man, however, the Doctor believed that getting bitten by a radioactive spider would result in radiation poisoning."
"Dan Slott once proposed a five issue limited series where Peter Parker would become The Doctor's travelling companion. While the BBC were enthusiastic about the idea, Slott's bosses at Marvel ultimately rejected the pitch."
So after all that I can conclude that Marvel are a bunch of pillocks and we missed out on possibly the coolest thing ever, The Doctor running about space and time with Spider-Man!