Seems like this problem is not fixed, right? Spent few hours installing and configuring everything, plugged in my S3, tuned everything up. It worked fast, I was happy. Than I just opened another browser (where there was no local cache for this website and I wasn't logged as admin to wp) and saw a white screen. Googled, and I'm here.
Disabled page cache. Working for now, needs some additional tests. But hey, why use W3TC if I can't cache pages?