Are you saying a device connected to an Ethernet socket can dial via the phone line the DSL is delivered over? If so, then I would say that isn't true. It may well do a VoIP connection via an external service but that would not rack up costs on the physical phone line the DSL is connected to.
The pair coming into the home provides POTS and a Broadband service. A hosted VoIP service uses the broadband leg so clearly the answer to your question is no.
My early posting was only to refute the statement that it was impossible to call a POTS number from a device that had only had a Ethernet connection. Nothing more.
However, calls made from such VoIP enabled devices using Zen's domestic VoIP offering gives a presentation number identical to the POTS number that the broadband service uses. Zen's rendered accounts are quite clear about call charges over POTS and VoIP but identify each in the public telephone service format so it would be quite easy, with a causal glance of the bill, to believe call charges were being racked up on the POTS service whereas they were really VoIP calls using the broadband provision.
Coming back to OPs original posting, he states that the only device connected to his router was the DVR device. If this is 100% true, then this posting has no reverence to his issue,