I just did some testing with this, and I have to conclude that it's far more character dependent than initially stated. Note that I did all tests with Ness as the target, not Lucas. Also note that this is generally a far less big deal than it is being made out as. Very low percentages and somewhat high percentages seem to have a fairly easy time doing the jump escape. As long as the Ness player is reasonably good at mashing, this will probably not ruin a matchup for him.
The following four characters can continue this combo unless interrupted by a jump break without moving: Charizard, Marth, Lucas, Snake.
That's it. If they just stand there mashing Z, anyone but those four is inescapable. Other than Lucas, the tether characters are too slow to regrab. Yoshi has the added quirk of ALWAYS being escaped with a jump escape so just add yet another disadvantage to Yoshi's ever growing list. That means we have this list:
Characters who cannot grab combo: Yoshi, Link, Toon Link, Samus, Zero Suit Samus, Olimar, Ivysaur
As per the other 28 characters, they are not feasible to test alone as their trick is a "step" version where they take a step forward (quickly so they slide) and grab Ness. For some it's far easier than for others. Squirtle seems to have the easiest regrab while Donkey Kong seems to have the hardest (DK's is almost certainly not forced). I cannot provide further testing here as I'd need another human trying his hardest to escape; those interesting in discovering just how much this matters to Ness should point their attention here. Also, I do not know if Lucas is the exact same; I did not test him.
EDIT: I just tested this with DK's cargo throw, and it is forced standing. Even more, it doesn't seem to allow a jump escape which means that Donkey Kong has an infinite combo against Ness and Lucas. I tested if this works against any other characters beside Ness and Lucas, and while the window to escape DK is very small, everyone else I tested could.