Can you do a traceroute to 8.8.4.4? If it's actually reaching Google's network, then yeah, they're doing deep packet inspection on DNS traffic. If not, they're probably just routing 8.8.4.4 to a DNS server they control. If their goal is to manipulate traffic to www.youtube.com (probably to block access to certain videos), another solution would be for YouTube to require SSL for all connections coming from Turkish IPs…
Actually this seems likely, hmmm: traceroute to 8.8.4.4 (8.8.4.4), 64 hops max, 52 byte packets 1 192.168.1.1 (192.168.1.1) 4.260 ms 0.969 ms 0.865 ms 2 host-92-44-0-42.reverse.superonline.net (92.44.0.42) 7.465 ms 7.903 ms 7.384 ms 3 host-82-222-174-177.reverse.superonline.net (82.222.174.177) 8.772 ms 13.703 ms 8.482 ms 4 host-85-29-17-234.reverse.superonline.net (85.29.17.234) 7.736 ms 7.830 ms host-82-222-35-54.r…
EDIT: More evidence that this is what's happening (they're doing to same to OpenDNS's anycast addresses): https://twitter.com/esesci/status/449902883933126659