Yeah it's true we say "help" but nobody is really gifting us wins, Everton definitely didn't. Teams wont be trying to beat Liverpool for our sake either, players raise themselves in games they know will have a lot of attention on them(felt like Walcott was doing that during the game for example). It's also that Liverpool are showing cracks now, they don't seem that invincible or that the football gods are quite as with them to some of the teams they have coming up, it's good timing really.
We can't get into the mindset that people want us to win that badly, we are just the lesser of two evils at best to most PL clubs supporters and they aren't the ones on the pitch. The players will still raise their games against us in high profile matches, just as they will against Liverpool, now that the title race has heated up. It's instant recognition, if you can fuck up someone's title tilt.