I got this flier in the mail, too.
They've had this for a while now, but it's only free for the first month.
The service costs 9.99, as you said, and the set-top converter runs an extra 3.00 on the bill. Additionally, even though you'd most likely be able to install the box yourself (unless the boxes have a protection scheme that only allows them to be initiated by the host office), expect the 20 dollar charge on your bill for "installation."
I think it's a damn good idea for those who just want rudimentary PVR capabilities...the units aren't particularly spacious, I don't think. The Cox FAQ mentions 50 hours as an "up to" time - not sure if that's the capacity of the unit, though.
HOWEVER, let's do a cost-analysis here:
This service appears inexpensive at first, but really isn't. It's 12.99 per month between the service and box, or 155.88 - plus applicable taxes (and you just KNOW somehow Cox has found a way to tax this...) It's not appreciably hard to find a TiVo unit for a decent price, and with store-bought units, you can alter the storage capacity (albeit at the cost of your warranty) to insanely high storage space on account of the Linux OS kernel taking HDs larger than 132GB.
At least with the store-bought units, you own the box and it's pretty much guaranteed to work in any place you hook it up, whereas the cable box wouldn't be - and if you move somewhere without cable PVR service, trust me, you're not going to be happy - you learn to rely on the damn thing. The monthly fee is pretty much the same and TiVo still has the lifetime subscription fee in place. The only downside is that it's another remote, but they're typically universal and programmable anyway.
IMO, you're better off with a standalone box. More expansion opportunities since HDs are dirt cheap now. Plus I expect the prices on regular TiVo and TiVo 2 units to hit the floor whenever the HD-compliant models start hitting.