Not likely. Why would they? I bet they are just too lazy to investigate this. One more customer, one less, who cares?
It's link IP address. Technically, IPs are generally needed to only terminate connections, but to forward packets IP isn't used any way. When you set up default route like "default via 192.168.1.1", this 192.168.1.1 only used to record NIC behind which the gateway exists and gateway's MAC address to send Ethernet packet; the IP address of the gateway itself is never used. Also the gateway isn't able to understand how your packet reached it. So you can use any address for that, as long as NIC and MAC happen to be the same, or use no address at all (provided you have a fancy networking stack that is able to be directly set up like this).
The same is in Internet. Operators need IP addresses on their routers; they are used to establish BGP (routing protocol) sessions to exchange routes, and when the RIB entry is selected to be added into the FIB, to provide a "target" NIC and MAC for the FIB entry (i.e. "to create a route"). Normally, nobody sees them, since they aren't used when forwarding. These are often called "link addresses". And, this also means that link addresses technically don't need to be public, so some administrators choose to use private addresses, to conserve precious public IPv4 addresses.
But it all changes when the forwarding system (router) needs to actually originate a packet. A ICMP TTL Exceeded message requires an originator IP address, and the router has nothing else than to put it's link address into the packet. This is the only way you happen to see its link address at all.
- The mentioned BGP builds the upper level route, expressed as a list of AS (autonomous system) numbers to traverse, in such a way so the same AS won't be entered twice. But ISP networks can more complex and logically partitioned into several ASs. In that case, the concept of "exiting and reentering" isn't that simple, it's not "a single network" anymore from Internet standpoint.
The trace shows #10 may have problems, but it doesn't necessarily means it does have them. For instance, systems process ICMP at a least privilege, they freely drop or ignore them if they have actual work to do. It's like a hint, showing to administrators where to start searching. For you, a hint may be that since the hops past this one don't show similar problems, the forwarding in the #10 happens normally, and its packets loss indicates ICMP throttling rather than problems. If there was a steady increase of the packet loss after some hop, that would mean there is something with that hop (or the link before it).
I've had similar situation, it was in a business setup (e.g. an organization suffered), it lasted for more than a year, and we only get to resolve it by chance when one of our past employees happened to move to work for that ISP for a brief period and they voluntarily initiated the investigation.
So, if you have any way to press them, do it. Read your contract, and so on.
If VPN works better, you may better off be solving this by actually requesting the VPN to be installed on your laptop. Show your administrators this trace, explain your experiences, write a note to your manager that the networking problems you have may prevent you from working efficiently, but that it may be solved with VPN, to grease bureaucratic wheels in your organization to turn faster.
