When there was a legal scrimmage kick on third down and K recovers and is downed behind the neutral zone then the next down will be 4th. K is not awarded a new series but neither is R. So K is in possession of the ball at the end of the play and will also be the next to put the ball in play but no new series is awarded.
So if you remove one of these requirements then you make this play a PSK enforcement when it never should be. Now if you consider the kick by K "giving up possession" then this is not a problem but NF says K is still in possession until R is in possession.
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