Verizon to level3: "Our traffic from netflix moved over to Level3 last night... very strange, anyways we need to increase our capacity..."
Level3 to Verizon: "Ok, that will be $X"
Verizon to level3: "um... That's 300% higher than any other provider out there..."
Level3 to Verizon: "suck it... your monies are belong to us"
Except that this fictional exchange you've created, in which Level 3 is extorting Verizon for more, is easily refuted by using either blog post. For instance, from Verizon:
Netflix did not make arrangements to deliver this massive amount of traffic through connections that can handle it.
[...] Netflix is responsible for either using connections that can carry the volume of traffic it is sending, or working out arrangements with its suppliers so they can handle the volumes. As we’ve made clear before, we regularly negotiate reasonable commercial arrangements with transit providers or content providers to ensure a level of capacity that accommodates their volume of traffic.
Which is a nice way of saying, "Level 3 is refusing to negotiate rates for more capacity with us, so we've refused to give them more." Level 3's blog post also affirms that the issue is Verizon's refusal to act:
Verizon has confirmed that everything between that router in their network and their subscribers is uncongested – in fact has plenty of capacity sitting there waiting to be used. Above, I confirmed exactly the same thing for the Level 3 network. So in fact, we could fix this congestion in about five minutes simply by connecting up more 10Gbps ports on those routers. Simple. Something we’ve been asking Verizon to do for many, many months, and something other providers regularly do in similar circumstances. But Verizon has refused.
Even without the blog posts, it should be obvious your notion makes little business sense. Level 3 is in no business position to play hardball like you've suggested. If they sacrificed on performance as a ploy to double-dip (i.e. get both Netflix and a lower-tier ISP* like Verizon to pay), Netflix would simply take its traffic to a different Tier 1 ISP that doesn't play those sorts of games, since the double-dipping would be hurting their bottom line. Or, at the very least, they'd be calling out their own ISP, rather than calling out the customer's ISP.
On the other hand, as a lower-tier ISP, Verizon has a monopoly on its own end users: if you want to reach them, you MUST go through them. If Verizon tries to double-dip by getting money out of both the higher-tier ISP and its end users, the end users won't understand what's going on, and in many cases they lack any viable alternatives anyway. Meanwhile, the higher-tier ISP can't switch out for a different peer, since Verizon is the only way to get to those end users.
Besides which, it's not like Netflix's switch from Akamai to Level 3 took Verizon by surprise, as you suggest, since it happened way back in 2010 and has been working fine for most of that time. If there was a problem resulting from the switch, it would have come up before now. Which is to say, this isn't a "Wow! Level 3's traffic is suddenly skyrocketing and we can't keep up!" situation. Rather, it's almost certainly a, "Hey, that Comcast company had a good idea to try getting money out of both sides...let's see if we can do it too!" situation, given the timing of it all.
* A quick aside: I'm well aware that Verizon also maintains a Tier 1 network, but Tier 1 networks rarely connect directly to end users. That's what lower-tier networks do. Moreover, the defining characteristic of a Tier 1 network is that it enjoys free peering with other Tier 1 networks. As such, the Verizon network being discussed here is clearly not their Tier 1 network, but rather a lower-tier one they control (e.g. a Tier 2 or 3 network) that has direct access to their end customers.