Do NOT connect things like in the second diagram.
As long as you are using LEDs, you would be OK, but if you loaded up a few channels with power hungry devices, you could exceed the current rating for the channel 1 neutral terminal (the input terminals are larger so that they can carry more current than the output terminals, also you would be grounding all channels through that terminal, which is not fused - the fuse is on the hot side with the assumption that only current that flowed through that fuse would be returning through the channel neutrals on that side).
You do need to hook the neutral to the input terminal on the right side. Not only are those snubbers not performing their intended function, without the neutral they could be allowing current to flow from channels on that side of the board that are "on" to the "off" channels.
On the board, if you flip it over and look at the back, you can see the heavy copy trace that directly connects the input terminal neutral to the 8 output neutral terminals on that half of the board. Whether you use the output neutral or not should not make any difference as long as the neutral you use for the strings is connected back to the same neutral that feeds the input terminal on the board.
RM