Lately Verizon has been pushing DSL folks to opt-out of a Carrier Grade NAT setup, which in essence can act as a "proxy" of sorts in a sense that many (hundreds) users come from a common IP address. This shouldn't apply to FiOS, but it may be something to consider if Verizon has recently started to take advantage of CGNAT.
Away from that, would it be possible to share the traceroute results? I've never seen proxy-like behavior even on my DSL connection, which has been opted out of Carrier Grade NAT since I use applications that will break behind CGNAT. When sharing the traces, please filter out anything sensitive so the moderators don't have to do it for you. Alternatively, you can send me an unedited trace via PM so it isn't floating around on the public forums.
Also, I'm sure you've checked all of this already, but please be sure to verify the Blu-Ray player or other devices on your network are not going through a proxy, or are set up behind a VPN or IPv6 tunnel.