Cloudflare doesn't host websites, it's a distributed caching proxy service for speed and DDoS protection, plus DNS services.
Oh, you're right, I thought they provided hosting as well. Then I'm not sure who the provider is, I read something about servers seized in the US at least, but can't find the link at the moment. Might just have been cached CDN files for the site or similar, who knows.
This article seems to suggest that they were'nt US based:
https://news.bitcoin.com/btc-e-closure-clients-are-mt-goxed-by-the-u-s-a-new-front-in-crypto-wars/For the first time, the U.S. government attacked a foreign exchange on foreign soil. It closed down the Russian-based exchange BTC-e. (Russian-based refers to ownership, not location.) BTC-e reported, On July 25
the FBI staff came to the data center
and seized all equipment, the servers contained databases and purses of our service. BTC-e is charged with 21 violations of U.S. financial law; the Financial Crimes Enforcement Network also hit it with a $110,003,314 penalty. The move was stunning not only because BTC-e is one of the oldest and largest exchanges but also because many now locked accounts are owned by U.S. citizens, non-residents.