If it is a normal fitting, both ends of the fitting will fit in the pump!
I have used a fitting meant to be a tube union fitting,
inotherwords to connect two flared tubes together.
I'll try to get some pix up soon.
The only thing I can think of is maybe his early fitting is a tapered pipe thread
where it screws into the pump.
but like you, I think a parker man should of picked up on that.