transvaal:
There is no way a double gun with the Rigby-Bissell rising bite, sans under-bolt, could be opened without operating the top-lever. Its a real bite alright!

Not guaranteeing the rising bite alone could cope with the pressure of firing, but I strongly suspect it would. Same with most other third bites.

I do agree that the screw-grip is unquestionably the strongest, due in part to the Webley "A&W C" long-bar action that featured it, but cross-bolts can be built strongly too.

...and don't forget the Westley Richards C-bolt guns that were built without any under-bolting whatsoever. What we might regard today as a doll's head with third bite was in fact the first and only bite in that case!

Action strength is all relative anyway:
I have a Rigby rising-bite double, a Webley screw-grip .577, a bunch of cross-bolted doubles (mostly Greeners but a couple of Cashmores and a few others), a Jeffery double with third bite on the dolls-head, even a Dougal lock-fast. And plenty with nothing more than the Purdey under-bolt. They were all strong enough to pass proof and all still lock up tight today, in some cases more than a century later.

And that is simply marvellous!