Going to spout off here… lol
If its a true corner, then all the points touch and you could cross without touching either private side. Or they could argue you touch both private pieces at the same time as touching both public pieces. Its all, or its nothing.
The argument that the two private pieces touch, therefore keeping you out, is a fallacy. It can be flipped to say that the two public pieces touch too then, letting you in.
If none of the pieces touch and its an infinite point in the middle, then again, you do not trespass by crossing. Its a no mans land.
Whether or not a kangaroo court and its jesters see it this way is another story. Think of it mathematically though, and from that standpoint it makes sense to be able to cross. It would be really nice if the landowners just left a little gap or just didnt care. Their biggest issue is probably people just breaking their fence or wrecking the land with trash. Just be prepared to deal with the consequences, but personally I would do it regardless.