From a more culinary perspective, you do probably want some fat in your burger. Depending on your tastes, I'm not sure the presence of 'plant matter' is particularly sinister either; I, for one, like a few onions in mine.
Those numbers should be right about what you'd expect.
> Meat and poultry are composed of naturally occurring water, muscle, connective tissue, fat, and bone. People eat meat for the muscle. The muscle is approximately 75% water (although different cuts may have more or less water) and 20% protein, with the remaining 5% representing a combination of fat, carbohydrate, and minerals.
The protein/fat balance should be expected to be a bit off from straight muscle cuts, as it's typical for a burger to have fat added to the mix in.
It is unclear from the abstract whether they were measuring the entire hamburger, including the bun and other condiments, or just the burger portion.
[1] https://www.ncbi.nlm.nih.gov/pubmed/18995204
TLDR: "Meat content in the hamburgers ranged from 2.1% to 14.8% (median, 12.1%)."