Routing traffic via the VPN changes the path the traffic flows over, possibly avoiding routes that are saturated and (who knows) pending upgrade.
It's tempting to imagine the internet as a giant blob of fungible bandwidth, but in reality it's just a big mess of cables some of which are higher capacity than others. Assuming malice is fun, but there isn't enough data here to say one way or another.
I suspect that whats going on is that Netflix put the majority of their traffic on Level3 and Level3 is trying to charge Verizon an exorbitant rate for enough bandwidth to handle that peer. Verizon said "No" and told Netflix to go with another peer. So Verizon has plenty of bandwidth, Netflix has plenty of bandwidth... it's where those peers are located that's the problem. Level3 has been giving Netflix huge discounts to try and force ISPs into unfriendly peer agreements.
So yes, if you VPN'd out to somewhere else... somewhere that's not an ISP and place where Level3 isn't trying to screw people, then yes, you'd avoid the route in question and get great service. Move all of Verizons traffic that way and see what happens. Ignoring saturation of the peers... It would work until that VPN services peering agreements ran out and then they'd be getting the same treatment.
The FCC, ISPs and Netflix need to stop screwing with net neutrality and fix the god damn peering agreement process. I've been involved with them peripherally and they're like the wild west when the 2 sides can't agree on something.