Stop in for a cup of coffee

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.
Matt is correct. DSL has serious limitations. Distance from fiber end is the biggest one. A DSL signal degrades very quickly after about 6k feet. Now to get DSL to go further, they lower the max speed, max attainable. See, the more speed you try to push down the pair, the more it degrades. RF interference is the next biggest issue with DSL. Where as Coax is shielded, DSL run on twisted pairs. The tighter the twist the less RF interference you can get. However, not all of ATandT plant, or outside, wiring is twisted. I can go on and on, BUT DSL does not share bandwidth. Just the further you are, the worse it gets. Physics.