Liverpool haven't though. They've signed players from the tier below that of their rivals, hence they won't be getting near them this season. Although I agree with the point you're making, City don't count as any kind of comparison.
This could very well be the last summer where we have even a slight of chance of being in the position to overpay for top talent, next summer even that option could be out of reach.
We should have gone all out for Cahill, M'Vila, Hazard and Benzema in May. We could have recouped the money from sales throughout the summer. I actually believe Wenger wanted to do something along those lines, perhaps not that extravagant, but something similar, and is livid with how the club's buying team/Gazidis/the board have handled the summer.