The Grammy's does its best to recognize truly gifted and talented musicians, but there is a margin for subjectivity. If a musician's body of work isn't submitted for reviewal it will never make it to the reviewing session. Even if entered who decides who the "experts" are that place the songs into their respective categories to be voted on. If a song is in the wrong category, that could make all the difference. So its very subjective to say whether or not the Grammy's are able to recognize the best musicians. In my opinion they come pretty close.
The Grammy's seem to be a popularity contest at times. If someone sells a lot of records, they win awards, regardless of their musical talent. This is not to say that excellent musicians do not win from time to time, but in this day and age, you far more often see the likes of Kanye and Kesha winning awards for being popular and cool and not for their musical prowess.
I think award shows such as the Grammys tend to only recognize the musicians that are mainstream and well known. Very rarely do you see musicians from the Indie scene or other less popular genres being recognized. The Grammys are a show, to get ratings, to make money in ad revenue. They are going to remember that when choosing who to honor and who to invite to perform.
No, in the last years there have been a tendency of artists becoming famous not because of their real talent but because of other factors instead, such as physical appearance and willingness to show their bodies in musical videos in the case of women. It's not fair to recognize a well fit woman that shows some skin in a music video but has a poor vocal quality as a better musician than a serious lady that might be voluptuous but has jaw-dropping musical talent.