I'm trying to understand what this output from traceroute means. I changed the IP addresses for privacy but retained the public/private IP range distinction.

traceroute.db -e -n 10.1.1.9
traceroute to (10.1.1.9), 30 hops max, 60 byte packets
 1  10.0.0.1  0.596 ms  0.588 ms  0.577 ms
 2  10.0.0.2  1.032 ms  1.029 ms  1.084 ms
 3  10.0.0.3  3.360 ms  3.355 ms  3.338 ms
 4  23.0.0.4  3.974 ms  4.592 ms  4.584 ms
 5  23.0.0.5  13.442 ms  13.445 ms  13.434 ms
 6  45.0.0.6  13.195 ms  12.924 ms  12.913 ms
 7  67.0.0.7  52.088 ms  51.683 ms  52.040 ms
 8  10.1.1.8  46.878 ms  44.575 ms  44.815 ms
 9  10.1.1.9  45.932 ms  45.603 ms  45.593 ms

The first 10.0.* range is inside my organisation. The last 10.1.* range is another site of my organisation. The intermediate addresses belong to various ISPs. I expect that there is some kind of VPN between the two sites, but I don't know much about our network topology.

What I don't understand is how the route can go from a private address through public addresses back into private addresses. Searching led me to Public IPs on MPLS Traceroute, which gives a possible explanation: MPLS. Is MPLS the only possible or most likely explanation? Otherwise what does this tell me about our network infrastructure?

Bonus question for my edification: in this scenario, who is generating the ICMP TTL exceeded packets and if relevant mangling their source and destination addresses?