Well, the "almighty" wordpress obviously is a little smarter than you, eh? Guess you didn't read where I said that without that, the system has no way to distinguish between a category on the main blog, and a username in subdirectory mode.
Every hit would have to not only query the main sites tables first, but then continue on with everything else.
So, to make it more efficient and reduce overhead, /blog is where the main sites blog resides.
You say you want a blog at /blog. OK, and the problem is? I mean, duh, that's what it is. It's a blog. If you can't make it work, then you're being very creative.
Admin blog = Main site = root mu = blog id 1...
And honestly, MU is overkill for 2 blogs. It's made for hundreds, thousands, tens of thousands...
It also has other things built into it which I'm sure you'll not bother to read or look into first, which you'll probably come back here and smack up the kind people who have busted their chops to give you this for free.
This isn't drupal, or the almighty anything.
Your best bet: Run, don't walk, to wordpress.com. Your "client" may not know it yet, but they'll thank you in the long run.