That is an almost legal foldover. She is correct in that it is a foldover, and that is the rule that should be cited here. A foldover can go from one set of bases to another set of catchers. Nothing in 3.3.6.c.1 says “original”. It begins from prep level and does not stop. It is caught on the back of the top person by multiple catchers, as defined in “foldover”. All of those parts of the rule requirements are in place.
The part that is not in place is the part the coach questioned. The people responsible for catching the top person are in the process of catching the person holding the foot at the time when the movement to the inversion is initiated. If someone were to get caught up during that catch, the top person is still going over and would be inverted and on her back. In fact, you can see the right side group moving to get in position to catch. Again, if they hit someone while going through because of a misalignment, there would be a major safety problem on the way down. I know it takes away from the visual they are trying to achieve, but I think they need to wait one or two counts in that prep hitch position so the catchers can take a step or two to be in position when they dip for the foldover. One “pump” at prep level might do the trick.