Not even a bit? You don't think someone who writes might be a better judge of others' writing? Or if someone wrestles, they might be in a better position to grade others' technique? Etc...
Not particularly, no.
Let me use myself as an example.
I've written a bit myself, but by my own (repeated)admission, I'm not a writer, and I have no interest whatsoever, in being a writer. So what qualifies me to judge good writing from bad?
I've been reading for more than 23 years. And my standards for quality have been steadily rising.
I've been reading fanfiction for more than 10 years, reviewing fanfics, working as a beta-reader, etc. Helping fanfiction writers improve their work. Because when I read fanfiction, I want to read quality work.
When I look at some of the fanfiction that I put on my favorites back when I started reading fanfics, I can only shake my head 'cause "bloody hell!, that's some shitty fics." A good example is a HP fic called the Ascension of the Scorpion Sorcerer. Back when I first read it, I thought it was bloody brilliant. When I went through my favorites a few months back, I couldn't even get past the first two chapters, the writing was bloody awful. The spelling was sporadic, the grammar was shot to hell, the plot was sketchy at best, and the characters flat and uninteresting.
Now, despite (again, by my own repeated admission)not being a writer. I'm pretty confident in saying that I can judge quality writing from poor writing. Are there others that are better at it? Sure, there's always someone better. Is it because they're writers? In some cases, probably, but definitely not all(an australian friend of mine called Daniel, is a great example. The guy is a friggin' grammar *uncreative*, but he's even less of a writer than I am).
Bottom Line: Saying that you have to be a writer, to be able to properly judge good writing from bad, is pure bullshit.