There are three reasons why our rise has leveled the playing field more than would otherwise be the case.
The first reason is that we have destabilised the established 'Big 4' in footballing terms, most especially united and Liverpool. You say we've not played a 'direct' role, which I partly disagree with, but it's a moot point. Our influence has made them behave differently, but more importantly has punished them for operating anachronistically, which I don't believe they would have been as severely if it wasn't for our influence and presence. We've created a level of chaos which has made them less impenetrable as footballing institutions. They've made bad decisions because we've been breathing down their neck, Van Persie being a case in point.
Secondly, we've made the Premier League 'product' discernibly more interesting, which in turn has imposed itself greatly on the new TV deals. The Premier League TV deal has leveled the paying field enormously within the top flight (although not in relation to the leagues below it, somewhat lamentably). It has closed the gap between the likes of Stoke and Everton and the ancien régime clubs. Moreover it has enabled clubs like Spurs and West Ham to be more bold with their stadium expansion plans, which in turn will act as a further leveler. There is no doubt in my mind that the 'product' would have been much less enticing had it been the same four clubs monopolising the top four places. Commercial inertia would have set in to a certain extent, and furthermore, levels of discontent among supporters of clubs outside that grouping would have been higher than is presently the case. As a consequence the Premier League would have been much less at ease with itself, which in turn would have diminished the league's intrinsic value. Simply, if the new TV deal wasn't as lucrative overall, the playing field would have been manifestly less even.
Thirdly, we have eroded the power base of those established clubs off the pitch as well. Who's to know whether they wouldn't have held the rest of the clubs to ransom in some way, like the Spanish pair did. That FFP letter is evidence of how far some of those clubs were prepared to go in terms of protectionism; united have form in recent years for trying to change the TV deal when Peter Kenyon was chairman, so although by definition this limb is more speculative, I believe it doesn't require a huge leap of imagination to conclude that without our presence the 'big 4' would have felt sufficiently emboldened to skew the TV deal increasingly in their favour, by increments, no doubt. It's certainly something they have form for over several decades.
In saying all this I don't believe that we have acted in a way that is remotely altruistic, or that in a crude, simplistic sense we've done much more than merely replaced Liverpool in an Animal Farm, 'two legs good, four legs better' kind of way, but you have to look beyond that and consider how the universe operates.
We've introduced a healthy level of chaos into a world that had become stultifyingly predictable. We've moved the pieces on the board, which has in turn enabled other clubs to profit. We've changed the landscape immensely; how can that not have impacted on clubs other than ourselves? That isn't how the world works. Look at the Scottish referendum and the impact that had on the outcome of the last general election. Or the influence that punk rock had on the wider British music scene. You cannot look at supervening events in isolation; their reach and scope extends well beyond what is immediately apparent.
Just because what you see this season is a by-product of our influence, rather than something that was intended, doesn't make that influence any less germane.
Edit: I should add that a further by-product of the new TV deal is that it has made qualifying for the Champions League less of a game changer than hitherto . Under previous deals, the thirty million quid clubs got for finishing in the top four acted as cushion in the form of a self-perpetuating cartel, as that sum meant those four clubs could easily keep the rest at arm's length in terms of player recruitment etc.. The gap was unbridgeable. The new Sky deal has significantly diluted that advantage. In actual fact, in a very real sense, the 'Sky 4' had a vested interest in suppressing the domestic TV deal to a certain extent, especially given that even as it previously stood it was still significantly more lucrative than any other in word football. In its previous format it gave them a simultaneous advantage over both their domestic and European rivals, which is not so profoundly the case with the new deal.