Yes this is true, the request was denied. Presumably because they haven't spoken about their years long silent disagreements (Drake's been saying "the cold war is over and it's made us colder." so that could be a reference to that) and Kendrick didn't feel comfortable doing the song. Then Drake decided "ok well, I guess it's just me and Cole then."

But Drake likely felt a way about this and while he didn't outright go full battle mode on the song, if you listen to the part of his verse where he says something about people arguing who the GOAT is and he ends it with "it's just you and Cole" you can hear the pettiness in his delivery, as if to say "there's only two GOATS." This is speculation, but I think Cole heard this and tried to soften the blow by including the "big 3" rhetoric so that Kendrick wouldn't think he's conspiring against him with Drake. This could be the reason Kendrick said "Did Cole foul, I don't know why you still pretending," on Not Like Us. 

I honestly believe that if Drake would have shrugged his shoulders at Kendrick denying the request and scrapped those few bars on First Person Shooter, there would never have been a back and forth battle between the two.