Yes they did have servers in the USA but only according to the "world police" USA.

PDF of the indictment is here: btc-e indictment (click the link "Download Vinnik Superseding Indictment Redacted" at the very bottom of the page).

So now, please define "server".

BTC-e.com had a lot of servers in multiple countries. It was not only cloudfare.com but also for example pusher.com (api for realtime trading data to extend the (polling) REST api).

Now, if BTC-e delegated (outsourced!) some parts of its service to services like cloudflare or pusher, did they themself operate servers in the USA?

That is the question.

You can make the comparison with Swiss banks.

Swiss banks (UBS and others) actually did send their employees to the USA, they acted within US territory and hence in that case the Swiss banks and the according employees were really guilty.

But in the case of BTC-e, running some btc-e servers located in USA without any BTC-e staff on site I cannot see any infringement.