Song lines

I have always wondered why Paul Bloody Simon called one of his songs "The 59th Street Bridge Song" rather than using its more famous and catchy subtitle.
One of my correspondents tells me it's because the eventually-popular (but now thankfully forgotten) line wasn't in the original version.
This is why:

In the 60s and 70s it was etiquette to order sumptuous room service for groupies.
Some of the more impecunious of the latter would apparently hang out with completely unshaggable rock/pop stars just for the food and drink.
And S&G were right at the top of the dead root list.
I mean, you could lose Simon in a decent sized hotel bed; and how do you think Artie could get that top Ab in "Bridge Over Troubled Water"?
Still the pair enjoyed their forays plucking ripe fruits in the garden of Venus, so Paulie wrote a song about it.
The first verse went:
"Slow down, you're moving too fast
"You gotta make the moaning last
"Skinny Artie's lost a stone
"Fucking for fun and feedin' groupies".