Ah. Yeah, that's a good reason to replace the socket.
There are lots of different looking neckboard sockets - usually they just differ by the way the focus wire attaches to them, or are just different brands. These two appear to be almost exactly the same thing, just probably made at different times for different markets, and probably slightly differ somehow, like wall thickness or pin length or something simple. All neckboard sockets just connect straight down to the board though, there aren't any that cross the pins around - that would be silly and expensive to make.
There are even a couple of tubes that have the same pinout but different socket connectors... so you can cheat and replace the neck socket on the arcade board with the one from the TV you took the tube from, if you run into one of those tubes in a swap.
Similarly, some neckboards have the traces and holes drilled for both narrow and large neck tubes, and you can usually swap the socket to use the chassis on one or the other type tube (assuming you have a compatible yoke).
-Ian