ATC question about helicopter routes

I've been flying on helicopetr routes over NYC for years now with
terrific controllers everywhere but got hung up with a controller last
week and I need help understanding his arguments for refusing me
access. He said I'm not a helicopter so I cannot fly a helicopter
route when it 'may' interfere with his separation requirements for
landing aircraft. Specifically, I wanted to fly from the Hudson across
the Park and then down the East River at 1000' or 1500'. He said as a
fixed-wing he was unable to allow this as he was landing ILS 4 at La
Guardia and couldn't get the necessary aircraft separation. I said
I'll be staying far west along the river but he still said he couldn't.
I then chose to be in the exclusion zone at the 59th street bridge
(play seaplane) and then he came back and said I could 'proceed as
requested initially' as he had someone 45 miles away on the ILS.

What's the real scoop about fixed-wing flying along these routes ?

Thanx.