Don’t worry. There is no spying occuring!
Just a quick post to clear something up.
Site stats have shown lots of interest from this post;
http://community.bt.com/t5/BT-Infinity/usa-department-of-defense-spying-on-infinity-users/td-p/578197
Which seems related to this post;
http://forums.thinkbroadband.com/fibre/4107499-alert-in-modem-log.html
Just to clear up any confusion, the following address ranges are private;
10.0.0.0/8
172.16.0.0/12
192.168.0.0/16
That is, you can’t use them on ‘The Internet’, they belong only in private home/business/management networks behind a real public IP (such as your home 192.168.0.x network behind one real internet IP).
The network I have discussed is a private network, it’s internal to the Infinity network, it’s directly attached (via the 301 VLAN) to your devices.
The reason it’s registered to the US DoD in ‘Who Is’ lookups is historic and dates back to Arpa-net. It’s the same historic stuff as why your IPv4 reverse DNS PTR records all end in ‘in-addr.arpa’
Further reading;
https://en.wikipedia.org/wiki/Private_network
It has (and let me be quite clear here before this blog attracts more attention that it ever wanted) NOTHING TO DO with the USA or related parties doing ANYTHING to BT Infinity connections or data.
That is all.
On an unrelated note however, the IPS logs in the second link are quite interesting from the perspective of return SNMP traffic, more later!
Through Infinity; and beyond? 
Yep, one of the IPs (the source IP) in the log is an internal nonroutable IP address. BTs SNMP querying servers are in this range.
The IP address that the VDSL modem has assigned by DHCP on its “BT management interface” is a “routable” 30.X IP address!
Connection Name IP Address Subnet Mask Default Gateway
ptm1.301 30.119.X.X 255.255.248.0 30.119.X.X
Why would BT be assigning a routable (and not even owned by them!) address to VDSL modems? Seems more sensible to be using (as you note) the local private IP addresses for their CPE management network IPs.
I realise that it’s unlikely to cause problems to the end user as the modem is just bridged and can’t “usurp” traffic to that subnet.. but from a technical point of view it seems a bit weird.