As reffred to in the text ,as you say ,Kathleen.

He might have been a first,second cousin or, indeed, even more distantly related than that.Cetainly cousin does not have to mean a first cousin ;-)

But he definately is some form of cousin to Mr Bennet according to the text.

To inherit , he must have descened in direct line from a male relation of Mr Bennets- his brother or, perhaps his brothers son,therby making him a scond cousin.

What he could not have done was to descend down the female line- for example, a sister of Mr Bennet,or an aunt.As the entail would not have allowed it,as it was limited to descent of males.The issue of females would not have counted- hence Mr Bennest girls could not inherit ;-)

The legal effect is the same, be it first or second or whatever cousin.The difference in name could be explained thus.