It's been a while since I looked into the this plugin's code. If I remember correctly, it should be pretty easy to do the switch to wp_remote_get() and that I used it when making some of my first patches for the plugin before later converting the patches to use cURL to be more consistent with the rest of the plugin.
If you have a bit of PHP experience you might be able to do the switch to wp_remote_get() yourself. Activating libcurl should be equally easy depending on your server policies.
Before doing further tweaking it might be worth getting a copy of the 2.0 beta in case it has solved the issue already: http://wordpress.org/support/topic/video-thumbnails-20-beta Giving a bit of feedback for that version should be most welcome too to get the final version out one day.