The answer to this question is...it depends. I was unsuccessful accessing through another ISP and was told, by Verizon tech support, that the ISP I was attempting to access through was blocking it. Now I guess that answer depends on how knowledgeable you believe Verizon tech support is?
On a side note...I've accessed espn3, when it was available through a previous provider, on different ISPs without issue.
When you visit the ESPN3 site, there should be a Sign In button or a "Watch Now" button that will ask you to log in using a Television provider or ISP's login details. For ESPN3/ESPN360 I do this at work when I wish to watch a sporting event that's available. click Watch Now, select Verizon Broadband, and log in using my Verizon account. My work is their own ISP so they do not use Verizon.
Now on a Verizon connection, it may be a different story but ESPN3 is starting to go more towards the stupid TV Everywhere model where you have to have an account to even access it. Gone are the days where you could get content just by having the proper ISP.
Can tell you it NEVER works at airports
To be expected. Airport Internet is usually mediocre because it is either on slow connectivity to begin with, has a ton of users on it, or the hotspot providers deny certain types of traffic over it.