Qualified for the $20 (only) hard drive with no $10 3-month Live subscription for my Arcade unit. Here is my setup and why I think it happened.
I have a Pro unit and an Arcade unit. I'm on my 4th Pro unit from the red ring so when I saw that I was able to get an Arcade unit on Amazon last December for like $200, I figured I'd just buy it as a backup. I have my Pro unit hooked up to my main TV and my Arcade hooked up to my PC (second monitor of my dual monitor set up). Both are connected to my router and my profile is stored on my memory card. I play on both my Arcade and my Pro (usually when my wife wants to watch TV, etc.) by moving my memory card back and forth, usually with the save files. My hard drive for my pro is where I just download demos and extra content but I still keep my main saves for everything on my 256 gig memory card so I can switch between consoles with no problems. As of this past weekend, I was already down to less than 100 megs on that memory card and I never hooked up my 20 gig HD to my Arcade unit.
Microsoft probably saw that I was a user connecting to Xbox Live on an Arcade Unit with a memory card with less than the required space needed for the update and gave me the offer of just the hard drive only. I believe that if I had more than 128 megs when they performed the check, I would be ineligible for the hard drive offer. Also, I'm guessing that if I had ever hooked up a hard drive to my Arcade unit prior to their check, I would also be ineligible because they'd assume I really actually had a hard drive. I have no idea how the $10 3 month Gold thing happens. I'm guessing that's if you connect to Live on your Arcade unit but aren't a gold subscriber?
Cliffnotes: Seems like if you play on an Arcade unit and connect to Live without ever having a hard drive connected to your system and your memory card has less than 128 megs remaining, you will be eligible for the hard drive update on your Arcade unit.