"Please explain why this is not limited to cash received..."
Because it IS an inversion and that's what the tax rules dictate.
"Please explain why ... basis carries over to the new stock?"
That question isn't clear but I assume you are asking why the new stock has a basis that's the same as the FMV of that stock on date of acquisition.
It's "as if" you were paid ENTIRELY IN CASH and then decided to take some part of that cash and buy some of the new stock. Hence the new stock has a basis of what you paid for it and a holding period that starts on the acquisition date.
