Batman,
Say your teammate shoots the ball, it hits the backboard (but not the rim) and you grab it and put it in. Are you giving your teammate an assist? Or a shot attempt and a rebound for you (even though, by your definition, since the shot clock would NOT have reset in that case, there was no shot)?
This should help set you straight:
http://209.85.165.104/search?q=cache:NE2MkR5uMeQJ:www.ncaa.org/library/statistical/basketball_stats_manual/2005/2005_basketball_stats.pdf+ncaa+basketball+statistics+handbook&hl=en&ct=clnk&cd=2&gl=us
Article 6. Blocked shots are counted as attempts when, in the opinion
of the statistician, the ball clearly was in flight before being blocked; or the
player was in the obvious act of shooting with the shooting hand moving
toward the basket; or the player was airborne and moving toward the bas-
ket with the intention of a dunk or layup and the ball in position for the shot.
If there is doubt about whether the player was in the act of shooting, the
interpretation shall be that he or she was not.
A.R. 6. Allen shoots and the shot is blocked by Brown. (a) Benton
gains control of the blocked shot; (b) Adams gains control of the
blocked shot; (c) Adams and Benton retrieve the ball simultaneous-
ly and a held ball is called; or (d) the ball goes out of bounds before
either team gains control. RULING: In (a), the statistician must
decide which was most important, the block by Brown or the efforts
of Benton to retrieve the blocked shot. If the statistician feels that the
block by Brown was most important, credit Brown with an individual
rebound. If the statistician feels that the efforts by Benton were most
important, credit Benton with the individual rebound. In (b), credit
Adams with an individual rebound. In (c), if Team A is awarded the
ball for a throw-in, credit Adams with an individual rebound. If Team
B is awarded the ball for a throw-in, credit either Brown or Benton
with an individual rebound. In (d), credit a team rebound to the team
that is awarded the ball for the throw-in. In all four cases, credit
Brown with a blocked shot.