Nit: If you're filing a flight plan, you do it with the country you're departing from. Even if you're piloting an aircraft departing into the US, it wouldn't have any effect on operations if you couldn't reach US websites. There's also several alternative ways for pilots to file flight plans outside of the web.

(The flight plans get passed between countries via AFTN/AMHS, which are dedicated telecommunications networks independent of the Internet.)