Actually, what he’s saying is factual. The real world on the other hand, has a tendency to play fast and loose with facts if it means political hay.
When the Mandate was established, it had roughly 118, 000 square kilometers of real estate. Everything east of the Jordan river was barred to Jews. Of that, about 77% would become Trans-Jordan, which was later renamed to The Hashemite Kingdom of Jordan.
Now, as the name implies, Trans-Jordan straddled both sides of the Jordan due to the end of the '48 war. This made the residents of the West Bank and Jerusalem, literally, Jordanians. In '67 they ‘became’ Palestinians.
But all that aside, of course the emergence of Palestinian nationalism means that they won’t move to Jordan in droves. However, the nature of the Mandate really does suggest that if this is about having adequate space and resources, that Jordan should be coughing some up as well. But, of course, we’ve had 60 years of Israel being expected to solve the problem and Arab states, even when they’ve kept Palesitnians in ghettos and instituted apartheid policies prohibiting Palestinians from living, working or immigrating into the main populace. Heck, do you remember the massive international outrage when when Jordan smashed Nahr el-Bared? Probably not, since there pretty much was none.
So it’s unlikely that “Israel must fix it!” will, at any time, really morph into “Israel and some of the Arab states must work to fix it.” But there’s a factual basis behind the idea that Jordan has a connection to the partitioning of Mandate territory.