All 19 NBA Development League teams are singly affiliated with an NBA franchise, but that does not mean that NBA franchises own exclusive rights to all of the players on their NBA D-League roster (like in Major League Baseball).
In fact, the majority of players in the NBA D-League are available for any of the 30 NBA teams to sign (call up); most NBADL players have signed contracts with the league rather than their individual team, so by NBA standards they are technically free agents.
This is why, for example, the Miami Heat could call up a Memphis Grizzlies “prospect” from the Grizzlies’ affiliate, the Iowa Energy. The Grizzlies may have identified prospects for the Iowa Energy roster, but these prospects are really auditioning for the entire NBA.
There are two types of players on NBADL rosters whose rights are exclusively owned by NBA teams:
1) Assignees — An NBA team can assign a player from its big-league roster to its NBADL affiliate. This player remains under contract with the assigning NBA team and can be recalled by only that team.
2) Draft Rights Players — An NBA team can acquire a player in the NBA Draft, decline to sign him to an NBA contract and instead allow him to sign with the NBA D-League. In that case, the NBA team’s NBADL affiliate can acquire that player directly, bypassing the usual NBA D-League player selection processes. (The most notable example of this came in 2014 with Thunder first-round pick Josh Huestis, who spent his entire rookie season with the Oklahoma City Blue.)
The other exception to this rule lies in players who enter the Development League as a path to the NBA Draft. NBADL players who still have NBA Draft eligibility cannot be called up to the NBA.