I think your response may have been colored by the oddly aggressive posts by the other forum members.
As you can see in that old quoted thread, it was asking a wholly different question unrelated to this one.
The router of this modem *is* running Linux with Busybox. Both of which are under the GPL v2 license. It is not a question of what OS the modem's router is running. That is already clearly available from the modem's syslog as I quoted in the original post.
For your reference:
Please do pass this on up your support channels.