In a tight match, I returned a ball that hit very close
to the line on the opposite side of the court from where my opponent stood.
He asked me if I thought it was in. I refused to tell him, informing him
that it was his call. Was I right?
No, you weren't. This type of situation comes up fairly often, and there is nothing in the official USTA rule book that covers many of these questions. So you might as well know the general rule when this happens. The USTA rules state, "When a match is played without officials the principles and guidelines set forth in the USTA Publication, The Code, shall apply in any situation not covered by the rules.
In this particular situation, the Code of Tennis states:
"It is both the obligation and prerogative of a player to call all shots landing on, or aimed at, his side of the net, to help his opponent make calls when the opponent requests it, and to call against himself (with the exception of a first service)."
So you were obligated to try to help your opponent make
the call.