The fact that someone covered a tune doesn’t mean much. That’s like saying Jimi Henrix wrote The Star Spangled Banner...
Different groups and singers cover songs over time. Most are familiar with the one that is done by someone in their generation. Back in the 60’s it was not unheard of to have a song done on the C&W, Pop/Rock and R&B charts all by different artists. Anyone that heard a song in ‘their style’ of music would say that their artist was the one they remember, regardless of who wrote it or who the ‘original artist’ was...................