Okay! So I am doing a fighting-only Nuzlocke on my White 2 file and I was doing the Pokestar Mission. I have a Riolu in my team and me, giddy with excitement, immediately played the script for Riolu Girl vs Brycen Man so that my Riolu will get a cute star animation whenever she's outta' ze Pokeball. However, my Riolu is rejected and I was forced to use the rental Pokemon instead -- which is also a Riolu by the way -- Why?
To make a film, the player must first choose whether to use a rental Pokémon or a Pokémon from their own party. However, the player is not allowed to use their party Pokémon in a film until they have filmed a Good Ending for it.
Good Ending - Generated by following the script. Creates a good, if predictable, ending. Getting the good ending usually unlocks the next movie in the series. The player can tell they are getting the good ending based on the pleased reactions of the director.
Soo... you need to use the rental Pokémon first, and then you can use your own Riolu (or any pokémon for that matter). Little tip, your Pokémon will only gain a star animation if they create a strange ending
Strange Ending (Japanese: カルトエンド Cult Ending) - Generated by deviating from the script a certain way, causing a puzzled response from the director. Strange endings change the nature of the movie entirely, generate a shocked reaction, and produce more box-office income than a good ending.
If the player manages to create a strange ending with their own Pokémon, their Pokémon will become a star and will be given a special entry animation, much like when a Shiny Pokémon is sent out.
Source: https://bulbapedia.bulbagarden.net/wiki/Pokéstar_Studios
In each individual script, you have to complete it once using the rental Pokemon before you're allowed to try it again using your own. The rentals have movesets specifically tuned for the story they're trying to tell, and bringing your own moves could vastly change the desired power level, making it either trivially easy or sometimes impossible to achieve the goal that the script is calling for.