With the exception of Square D QO breakers, all other double poles are simply the single pole breakers riveted together with a handle tie permanently made on to them. There is not internal connection between them. When one goes, it takes the other with it. You want both sides dead when you are going to work on the circuit and this is why the NEC requires the handle tie or double pole breaker. Fact is a double pole costs about the same price as two single poles, and you add in the price of a package of handle ties and its more expensive to use the single poles on the MWBC.
Handle ties are rigid metal or plastic pins that pass all the way thru the holes in the handles, or are metal sleeves that rigidly clamp on the handles. If one trips, it is going to take the other with it.
Its a mountains out of mole hills thing, just use the double pole breaker and be done with it or don't use the MWBC.
I'd be interested to see any manufacturers information you could provide that has information to the contrary.
Charles