This summary is not the rule. The rule text controls.
If someone died and a court in another state (their home state) already appointed a person to handle their affairs, Louisiana courts will normally give that same person priority to also be appointed as the representative here. This means if you're already handling an estate in another state, you get first consideration for the Louisiana appointment too.
There's an exception, though. If that person doesn't meet the qualifications spelled out in Article 3097, they lose this priority. In that case, the court will decide who gets appointed by following the standard rules in Article 3098 instead, just like it would for any other case where no outside appointment exists.
In simple terms, this rule tries to keep things consistent. If you're already trusted to manage someone's estate in their home state, Louisiana will usually let you continue that role here too, as long as you meet the basic requirements to serve.