Think about it...
Neutral is the return line. If it's shared, it's doing double duty.
Suppose Joe and Jodi are each enjoying 1.5 GPM showers. How much is going down the drain? Would you have any reason to think anything other than 3.0 GPM?
If Jim and Jana were each operating a 15 GPM hydraulic mill, and they shared a return pipe, would you believe for a minute the return line didn't handle 30 GPM?
So you know, intuitively, that something pretty special would have to be happening for the neutral to be carrying other than 30 amps. So you are exactly right to question this.
What special thing is happening?
You can't have negative hydraulic pressure (because you can't go below zero PSI or it'll just cavitate). But voltage is a completely different deal. Voltage can be any degree positive or negative.
Well now, suddenly we have an option. We can run Jim's tool on positive pressure, Jana's tool on negative pressure, and the most of the fluid does a "big loop" - through Jim's then Jana's tool, with the return line flowing two ways to even out any glitches and bumps. And now, we can use a return line rated 15 GPM instead of 30. But we have to do the positive/negative thing.
There's a flaw in this metaphor that turns out to be trivial. AC power reverses itself 120 times a second (in places MWBCs are common: this parenthetical is for the nitpickers). So, this positive/negative metaphor is misnamed. However, since all the voltages reverse at the same time, the metaphor is still valid, it's just correct half the time and neatly inverted half the time.
Several big dangers...
There's an obvious and serious blunder: It's very easy to wire up the circuit so that both hot legs are on the same pole. ("positive" in our flawed metaphor). In that case, yes, the neutral would carry 30A. You'd be able to test that by comparing the voltage of the two hots. If there is 0 volts between them (i.e. they are both positive at the same time), then they're pushing in the same direction and driving that neutral up to 30A. If there is 240V between them, then one is pushing while the other pulls, and we have the desired effect: Neutral only handles differential (imbalance) current.
Remember. Neutrals don't have breakers.
There's another danger anytime you have 2 circuits sharing wires or outlets: Imagine a worker needs to repair Jim and Jana's hydraulic return line. The worker carefully Lockout/Tagout's Jim's hydraulic line. Problem? Bigtime. Jana's tool is still live. So Jim and Jana's shutoff valves better be ganged.
... lead to very important rules
First, the breakers must be carefully phased to be opposite phases. This is where it helps to read about how breaker panels are internally phased. The two legs of the MWBC absolutely, positively, need to be 240V apart - never 0V apart. And if you read that whole Q&A you can see where "double-stuff" breakers are a huge problem here.
But the "necessity of phasing" issue intersects another problem: both legs need a ganged maintenance disconnect, such as a handle-tie or just being a 2-pole breaker. And here's the thing... on most panels (not GE), a factory handle-tie will also enforce correct phasing; it won't fit on breakers that are mis-phased for an MWBC. And on every panel, a 2-pole breaker will enforce correct phasing (unless you defeat the keying on a GE breaker, which people have done).
- Factory handle ties are notoriously difficult to find, and they also cost near as much as a breaker. Whereas 2-pole 15A and 20A breakers generally cost the same as 2 singles, so factory handle-ties are a waste of money and time IMO. Just use a 2-pole.
So, for both phasing and maintenance safety reasons, the two hots of any MWBC must be landed on a 2-pole breaker (or two singles with a factory handle-tie placed in the same position as a 2-pole).
2 circuits on the same yoke must also be handle-tied
Even if the above wasn't a rule, it's also a rule that when 2 circuits are on the same yoke (that split receptacle you mentioned), the 2 breakers must be handle-tied (or 2-pole). That's again to protect workers - typically a worker plugs in a radio and throws breakers off until the radio stops (turning all other breakers back on). That action MUST shut off the other circuit on that same yoke as well, so the worker doesn't get nailed by the other circuit.