Yep, the inside kind depends on the pipe being cut low enough that the flange can rest on it. Cut it too low and you don't have enough to get a bite on. The outside kind sit around the pipe and are a bit more forgiving in how low the flange can sit. You'd still want it low enough to avoid there being a place for waste to collect, but it's easier to gauge this when you can SEE how much pipe needs to be removed. Either way the flange itself is what gets screwed to the floor. The toilet is only held down to the flange by the closet bolts.
Added sturdiness around the flange can't hurt. It's not so much the weigh bearing down that's the issue, it's the side-to-side flex. If the flange screws have something beefy below to bite into you've got much less chance of that, especially if/when the subfloor gets wet and starts to rot..