According to :

This is possible.
Imagine the following counterexample.

two breakers in use
12-3 connected to both breakers (shared neutral)
15 A breaker on pole B in slot 2 of breaker box (red)
20 A breaker on pole A in slot 19 of breaker box (black)
12-3 wire runs to living room into junction box
15 A circuit from junction box feeds living room lights (red circuit)
20 A circuit from junction box feed living room receptacles (black
circuit)
12-3 continues on to bathroom into second junction box
15 A circuit from junction box feeds bathroom fan (red circuit)
20 A circuit from junction box feeds receptacles (black circuit)

If someone drove a nail through the shared neutral after the living
room but before the bathroom the living room would continue to work
(both circuits) but the bathroom would experience 240V and the fan /
GFCI receptacles might appear dead.

Something similar to that would happen, but not the way you describe.
On the side with a switched on device, the voltage would appear to be
zero (hot-neutral). On the side with _no_ switched on devices, the
voltage would appear to be 240V (hot-neutral). Hot-ground would be
120V.

If _both_ sides had something switched on, the _lighter_ load side
would see 120V (hot-neutral), and the _higher_ load side would
see 120V (hot-neutral). Hot-ground would be 120V.

And finally, if _nothing_ was switched on, a hot-neutral voltage
reading could be anything (neutral is floating), and a hot-ground
test would be 120V.

I suspect the real situation is that it's a simple 120V circuit,
the line itself is broken somewhere (instead of the breaker off), and he's
assuming that since what he already saw go off with one breaker,
and _now_ some of it is on, and some of it is off, that the original
fault was multiple breakers, and now he's seeing a single.

Or simply that he's forgetting which is which and has gotten
confused.

It certainly does seem like the circuit is overloaded (running
a vacuum AND A/C and other things on the same line is just asking
for it).

I'd assume it's a _single_ line break, ignore the previous
suppositions, and work at tracing exactly what the routing
really is. Checking for opens in the boxes is the right thing,
but it could be in a box that still seems live - hence tracing
may still be necessary.
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.