[mbyron]

We see this every season: "Is it POI or AP?" The question betrays a misunderstanding of POI that BITS and others have been trying to correct.

POI is a complex procedure for getting the ball back in play, and it includes as one of its possible procedures the AP arrow. In some cases, POI will invoke the AP arrow, in others it won't; the rule specifies which are which (not a judgment call).

Kudos to the OP for going to the rule book with this question, even though the approach is backwards. We don't want to look up all the times the AP is used and try to fit one to the situation given.

Instead, the order you want is: double foul -> POI -> definition of POI -> applicable provision. Since a throw-in was in progress when the DF was called, resume with the throw-in. Easy as pie.