I have experience working in the music industry, but I am not a lawyer, so keep both facts in mind when you read this (smile). Also, I'm probably telling you more than you want to know, but some may enjoy this.
You don't need to get permission to record or release a song that someone else has written and copyrighted. However, if you issue a recording of someone's song (or of your own, for that matter), the organizations that collect revenues for music must be alerted so they can track income and see that it is distributed to the proper parties.
There are two main categories of income from music performance: airplay (radio, TV, concerts, etc.) and sales (CD, albums, downloads, etc.). BMI, ASCAP and SESAC collect royalties for airplay, and other organizations collect it for sales and downloads (that gets a bit confusing, so I won't elaborate).
Once these groups collect royalties, they distribute it to songwriters, music publishers and record labels accordingly.
Note that the "musicians" who played on the above music are not included in the payment streams. They are paid for their work on the recording sessions and do not share in royalties. If someone wonders whether using Yamaha arranger song styles or parts of song styles in a new recording obligates them to pay royalties for these sounds, my guess (remember, I'm not a lawyer) is that these styles can be used without needing to pay Yamaha or whoever created the style.
You can copyright a lyric or a melody, and you can copyright a lyric combined with a melody, but you can't copyright the "feeling" that a style provides as a background while you create a new song or record your version of someone else's song.
On top of that, when you import a style to your arranger keyboard, in a great majority of cases thyere are tiny alterations made, for voices, etc., and it can be argued that a new style is created in that sense.
Hope this sheds a little light on things.