"Long count" handicaps in One Pocket
Pretty close, but only the player with the higher count would spot balls. In this case, the player needing sixteen would spot his first 8 balls. At this point they would both need 8. With only fifteen balls on the table, only one person could make their needed amount.
That is correct. And, the important thing to remember about the spot is that the spotting doesn't take place until *after* the player needing sixteen has pocketed his first 8 balls. Then, all 8 of those balls he just pocketed spot-up simultaneously, in a line, from the foot spot down to the cushion. This prevents the situation whereby the player sets up for an easy spot-shot (by cue ball control) after pocketing his 8th ball, spot up one ball, pocket that ball, control whitey to set up for another easy spot-shot (e.g. draw back a bit), spot-up another ball, pocket it, control whitey for another easy spot-shot (e.g. draw back a bit), spot up another ball, ...ad infinitum until all 8 balls that he/she previously pocketed, are pocketed again.
Simultaneous spotting of all 8 balls prevents that "gimme" situation. Here's a good table illustrating how to handle these "Long Count" situations:
http://onepocket.org/handicaps.htm
-Sean