I don't know what the exact issue is, but I will throw in two cents worth.

DSL uses "excess" bandwidth on the twisted pair copper phone wires
leaving your house. In this case, the "excess" bandwidth is starting
somewhere above 10KHz and going up to several Megahertz, typically well
above the AM broadcast band. The DSL signal starts just above the
usual telephone audio band and would be audible noise in your
telephone if you didn't use the filters they ship with the DSL modem.

I've had small transformers and inductors generate noise before,
particularly when it was tones above the usual voice range, and a kind
of "spiky" waveform. This is fairly common where the wire winding on
the transformer is a bit loose or where it wasn't painted with shellac
or something that would prevent vibration. As a quick fix, I've used a
layer of Crazy Glue to glue the wires in place so they couldn't
vibrate any more.

If there is a DSL filter built into the jack or there is a DSL filter
module attached at the wall jack, I wouldn't be too surprised if the
wire in one of the inductors in the filter was vibrating in time to
one of the DSL signal components and you could hear it in a quiet
room. It should tend to be just the high pitch sounds and would not
approach full fidelity, but I wouldn't find it hard to believe.

If you want hard to believe, I live less than 1 mile from the KSTP AM
towers in Maplewood. One time about 30 years ago, on a very quiet
summer night, I'd swear I was hearing KSTP audio from the rusty rain
gutters outside the kitchen windows. I suppose it could have been
coming from the hot water radiator under the windows.... I never did
figure out what that could have been vibrating to convert RF to air
movement....

Doug.