This is a tour de force of NEC violations, all due respect.
220v, existing 3-wire circuit, new 4-wire cooktop (I understand that white and ground on cooktop get connected to bare ground on incoming line).
Noooo, that's never true. Neutral is not ground. 4-wire cooktops are looking for neutral. 3-wire range connections provide hot-hot-neutral. A legal 3-wire range connection does not provide ground.
When a 3-wire range ties neutral to ground, what it is doing is supplying neutral in the normal way, and then bootlegging ground. This is a "legal bootleg" owing to an exception in Code at 250.140. The rationale is that these connections are rarely disturbed, and this will avoid interrupting appliance sales to underequipped locations. Sadly many of those locations are grounded but the installer does not recognize the metal conduit wiring method, so bootlegs.
BUT, the 3-wire incoming line first goes into a junction box which feeds a 220v, 3-wire undersink tankless water heater.
OK, a 3-wire feed to a 240V water heater is Hot-Hot-GROUND. Can you use that for a water heater? You betcha. Any NM-B type cable will be fine for that; just re-task the white wire to Hot L2, and use the bare ground for ground.
So stop right there. You're all set.
That same 3-wire line then goes to the new cooktop where the white neutral and ground are tied together.
Nope, can't do that. The circuit is oversubscribed. The total loads are too much for the circuit. You will need to run a separate cable for the cooktop. In some cases the cooktop and oven can share a cable. This cable MUST be /3. You would be well advised to use #6 or at least #8.
The cooktop has an integrated fan so I’m sure that the neutral and ground will be part of an active (i.e. “live”) 120v circuit.
Then it needs Neutral. Neutral specifically! Ground will not do.
Now, if you look at 230.140 Exception Condition 3, you can see that only insulated neutrals are allowed. With an exception for the webbed neutral found wrapped around the hots in SE cable. Your "Last Guy" is trying to play it both ways: use a grounded 2-wire Romex cable, call the bare ground a "neutral" even though that is specifically prohibited, then turn around and use it for a ground also. Can't do any of that.
QUESTION: is this dangerous? Logically if it was dangerous, any instructions suggesting tying the neutral and ground together would also state that the neutral and ground can ONLY be tied together on a dedicated circuit, which the instructions did not state.
It's always dangerous when neutral and ground are mixed. This was only permitted because the appliance manufacturers projected that there wouldn't be enough fatalities to justify slowing appliance sales. A simple wire break shouldn't make a circuit dangerous; however if a stove or dryer is "legally" wired, a neutral wire break will energize the chassis of the range or dryer. Because of this damn fool commingling of neutrals and grounds, a ground wire break will energize all the grounds in the area. And suddenly light switch screws are biting you.
