Was Luigi the savior of Sarasaland?

This is an odd concept, I know, but it makes sense. People ask "Why is Luigi absent from Suprt Mario Sunshine?" Easy answer: He gone on his own journey to save Daisy. Okay okay, you might remark that the manual for both Super Mario Land and it's sequel, The 6 Golden Coins, that Mario ventured to save Daisy. Well, in both Super Mario Odyssey and Paper Mario: The Thousand Year Door, Mario is able to dress as his green brother. I see no problem in going the other way. Here's how it'll be:

Luigi gets a letter stating that the leader of Sarasaland need Mario's help to save their beloved Daisy and he knew that he was going to go on vacation. He gets invited by Mario to in the vacation, but he turns it down with the escuse that he needs to make sure the kingdom stays safe in case of Bowser. Mario, Peach, Toadsworth, and some toads leave without any celebration because they don't want Bowser to find out and Luigi left a few days after the departure. He dressed as his older brother with spare clothes Mario didn't pack up, and ventured to Sarasaland to save Daisy. A while after saving her, Luigi revealed his identity after being under his brother's persona. She still stays with him.

This I thought of was that, although Daisy was saved by "Mario", she is known for being Luigi's girlfriend. Also, why is Luigi absent from Mario Sunshine?

"But Kyle!" I hear you type "What about 6 Golden Coins? The manual states that it's after Mario saved Sarasaland" Well... Mario IS egotistical at times, so he could just accept what the people say since the vacation of Sunshine was unknown to the public so Peach wouldn't be in danger if the Koopas found out, and the public though that it was Mario that saved Sarasaland and wait... Who writes the stories of battles? Oh yeah! THE VICTOR. Since everyone believed Mario saved Daisy, they written that he returned when Wario took over.