Summoning sickness ruling please

I haven't played Magic for a few years now.  However, recently I sat
down with a friend of my daughter and played him a few games.  He did
something I believe is illegal.  Here's how it went. 

During his turn, he plays a creature that requires to tap to do an
ability.  The creature suffers summoning sickness and he agrees to this
part of the situation. 

However, during my turn, he taps his "just summoned" creature and uses
its ability.  I told him he couldn't do that until the beginning of his
next turn.  He, however, informs me that the rules now say that a
creature suffers summoning sickness until the end of the caster's turn
and he can do its ability during the next player's turn. 

Example: Play a Royal Assassin.  It suffers summoning. But, during the
next player's turn, he taps the Assassin to kill a tapped creature the 
other player has. 

When I played all those years ago, the creature had to wait until my turn 
came around again to tap to do it's ability.  I'm not talking about 
creatures like Frozen Shades, that CAN be pumped up and doesn't need to tap 
to do it.

I've looked at the core rules and I can't find anything about summoning
or summoning sickness.  But still, I can't believe that the rules have
changed  on this particular situation.  Could someone give me a heads upon 
on this?

Please feel free to email me with your reply.