Grab my hand and walk with me on this one...
Luke played the same role to Percy, as Hal did to Luke.
So in 'The Diary of Luke', Hal ends up sacrificing himself to save Luke and Thalia. Leaving Luke with a request or promise for Luke to keep. For Luke to keep his will alive, and Luke excepts this and vows to try and do right by Hal and make the most of his sacrifice.
Luke starts to show more of his disdain for the gods, but overall there is no major, drastic change in him. Until he officially meets his father...
After that it is said by Thalia that he became more reckless and so full of rage. Making his hatred for the gods more known and noticable (and that probably got a bit worse after Thalia's "death"). And this is all a few years before his quest for the golden apple and when Kronos starts plaguing his dreams more, and slowly recruiting him. By then, he has been given plenty reason to become spiteful towards the gods and turn against them.
Now let's look at Percy and Luke's relationship.
In The Last Olympian, Luke ends up having to sacrifice himself to save Percy, Annabeth, Grover, and all of the other demigods left alive. The last thing he does is ask Percy to keep the promise to 'not let it happen again'. He asks Percy to keep his will alive and make things better for other demigods so that they won't have to go through what him and many others went through. Percy excepts this and promises to try and do right by Luke and not let his sacrifice be in vain.
Percy starts to show more disdain towards the gods (even before Luke's death) but overall, there was no major change in his opinion about the gods.
Until he gets abducted by Hera/ Juno to fight another war, leaving him on the streets for months without memories or barely an idea of who he was. After that, we see him show more hatred towards the gods (especially so in Tartarus). He shows more disdain for them, even mentions how he's starting to see Luke's point a lot clearer.
And with all of this, if Rick wanted to (if he wasn't a coward) between the events of the Giant war and with the loss of other friends, then the gods having the nerve to ask him to complete other quests? Yeah, Rick could easily have Percy officially turn against the gods and start his own rebellion in 'Chalice of the Gods'.
And this all happened/ could happen because of the role that Luke played to Percy. And absolutely none of those would happen if it weren't for Luke meeting Hal.