So, if you have Caching enabled on that virtual server, then the behaviour is explainable:
"When the Cache Setting feature (referred to as RAM Cache in BIG-IP versions prior to 11.0.0) is enabled on a virtual server, all server-side requests generated by that virtual server will use the HTTP/1.0 protocol. This also applies to server-side requests derived from an HTTP/1.1 client-side request; all HTTP/1.1 requests are rewritten to HTTP/1.0. A Connection: Keepalive header will be added to allow persistent server connections."
http://support.f5.com/kb/en-us/solutions/public/10000/400/sol10480.html?sr=34761170
"Also, how can I verify that indeed the virtual IP is making a http/1.0 request to the real servers?"
Tcpdump of something like:
If you have SNAT:
-- tcpdump -nni 0.0:nnn -s0 '(host ClientIP and host VirtServIP) or (host SNAT_IP and host PoolMember)' -w /var/tmp/capture.pcap
If you don't have SNAT
-- tcpdump -nni 0.0:nnn -s0 host ClientIP -w /var/tmp/capture.pcap
After that, open the capture file in wireshark and you should be able to see the request on ClientSide and ServerSide of the BIGIP (since it's a full proxy) and see how the client behaves.
If you don't have caching and the client is coming on HTTP/1.0 and you want to switch it, see this discussion:
https://devcentral.f5.com/questions/disable-http-10