It's not their responsibility, but they are losing business from it. And don't forget there is an ISP at both ends of the connection, and some have better links to the major transit providers than others.
Take any major service, like YouTube, Facebook, Twitter etc. They don't just plug a server into the internet and go "oh well if its slow for some people, never mind". They proactively think about how the content is delivered, where the bottlenecks are, work with transit providers and ISPs to improve routes, and generally do everything they can to make sure theproductsusers can access the service as seamlessly as possible.
If my internet connection doesn't suffer from high traffic and instability, but something along the route is going wrong for this particular game then who's responsibility is it? Unfortunately that is impossible to answer, you can't point the finger at any particular entity and go "it's their fault".
It's not SE's legal responsibility for every packet dropped between the players and the servers, and they don't need to do anything (this is very clearly demonstrated by the fact they haven't posted any follows ups or mentioned the issue at all since asking people to post reports with their ISP if they are experiencing lag). It would be nice if they looked into this and gave some updates on their investigation, showed they are monitoring QoS and how their data is being delivered, but that doesn't mean they have to.
I now have a workaround, the game is playable again, SE have said proxies are not a violation of ToS, and I don't mind paying more for an additional service, as it's still far less than I would have to pay in cancellation fees and setup fees to switch ISP (which may or may not have the same problem, no way to tell in advance).
It's a shame some people seem to enjoy mocking the victims so much, from their lag-free high horses.
(edit: Shioban sorry if it seems that last line is aimed at you, it isn't, your post was just a jumping off point to explain my view, it's for the people who claim there is no lag because they don't lag... you know who you are)