No, that is incorrect.
Let's look at a little frame data to illustrate this point:
Nana's Input Delay: 5 frames.
FThrow Frame Data: 24 Release / 50 IASA
Grab Frame Data: 6-7 Hit / 30 IASA
Let's assume you don't mess up anything. You tapped the stick at the right speed and stopped the "free" climber at the right position, and pressed grab at the right time. In regards to pressing grab, here's what happens:
Popo to Nana - Input FThrow on frame 1. Input Grab on frame 14, grab initiates on frame 19 due to Nana's delay. Grab connects on frame 24. Timing = 14 frames.
Nana to Popo - Input FThrow on frame 1, throw initiates on frame 6 due to Nana's delay. Input Grab on frame 24. Grab connects on frame 29. Timing = 24 frames.
It's a difference of 10 frames, easily noticeable to anyone. The difference is 10 frames regardless of the throw or victim in question. Compared to the hypothetical "Popo passing to Popo", regrabbing in Popo to Nana is always 5 frames early. In the same comparison, Nana to Popo is always 5 frames late. These are of course the earliest/perfect timings possible, in practice you usually get a good 4 or more frames of leeway unless the victim is at obscenely high percentages.
Incidentally, FThrow frame data is the same on all characters, but again, this example can be applied to any throw on any character (barring UThrow, obviously).