Before I read the 2nd post I was also going to say you would probably just compete with yourself for the phrase and the article site may outrank you pushing your blog down.
You could use a different combination of your main keywords in the article or sometimes just use them in a different order. OR think about using synonyms.
If your blog post was a long tail title including the main keywords dog training, make your article title about training your dog or puppy training. Letting your keyword research guide you, of course.
"Some of these searches are just plain bad grammar."
I've seen phrases like that, and I'm just not sure. I guess it would depend on the phrase. Also may be worth double checking to be sure it's not just showing up as a fluke on the KW tool you are using? So ck in both Wordtracker and Google KW tools to be sure it really has search volume?
Then maybe if you're sure it's worth pursuing but doesn't sound right, use that phrase on an article submission instead of having people raise their eyebrows on your blog.