Another good example is GitHub, which obviously uses git (pure GPL). But it is using git! Even if they have modified git to fit their purpose, it is not necessary to publish it back.
Given the above arguments, it is very clear that almost all of SaaS, and providing hosted services is using than distributing the application.
On the contrary if you are creating a package which allows people to create websites. that clearly falls under distribution - but this is not the case with you.
So I think you are safe. However, it is a very strong argument to defend on court. Because the very word distribution has different meaning in laws in different locales. Getting permission from the original author is your best bet.