Okay, let me take a look at what I have. Be back shortly.
My file size is 6,518,272 bytes (NOT size on disk), also identified as version 184.108.40.206 (how in the world does THAT work? LOL). BTW, I'm getting that info from right click -> properties on the executable. The version on the game's launch screen shows 1.153.
To fix the problem I had (Steam on the retail disk), I downloaded the complete game file (615,036,714 bytes) on 05 August 2012 from taleworlds.com, and it looks like this is the version still available on their site; note that I did not get the patch, but instead the full installer zip.
Maybe try this link, in case you're getting a different version somehow: http://download2.taleworlds.com/mb_warband_setup_1153.exe
I just DL'd again and got the same zip as last time.
But yeah, Steam isn't nagging me at all (it used to, until I reinstalled and then changed the shortcut), Steam is definitely no longer installed, and the game works. Not sure why you and I are seeing differing results.