Apologies I'd slightly misunderstood your question, I see exactly what you mean now. I think this is purely down to the way Google associates the search intent and tries to deliver the most appropriate result.
The site parameter is obviously intended to help users find a specific item on the specified site, therefore if the blog has more content than the other pages there is more chance that it will have what the user is looking for hence Google will deliver that page out of preference.
Don't know for sure but just an assumption.
As you said branded searches are fine, there certainly doesn't look to be any issues as far as I can see although I haven't done a full audit.
Would be interested to see what anyone else says but my gut feeling is there is nothing to be worried about, the main thing is you come up for your company name and search terms that you want.
Sorry hope that helps somewhat.
All the best