Tim might know more.
I think you got a AT&T lackey reading from a script. DSL sends packets on the same wires the analog current carrying voice. The final leg from the exchange should not be shared - it just might be long, old, and oxidized or have bad connections.
Cable service does share the line - almost to the house. If it makes you feel better, everyone suffers when there is high demand. That's one of the complaints with cable here. They need to go to those better lines, whatever they are, if they're planning to be competitive against FIOS and soon or later, 5G.