That's exactly what he's saying. The NYS&W built the connector, and owns it; NS owns the trackage at both ends.
(The new switch on the former Graham Line is called HJ, for Hudson Junction; to me, it's 'new' HJ; the real Hudson Junction was on the L&HR between East Chester and Greycourt, where the original Warwick Valley RR line branched off from the Orange County RR to Maybrook- both components of the L&HR.)
And you won't find Pelton Road on any map newer than about 1971; since then it's been the Orange County Route 1 crossing, at the south end of the former Warwick yards.