I'm accounting the tablet in the personal computers and the stuff it prints off in the imaging and printing. I think it's fair to say those items fit into the respective categories.
HP isn't trying to influence business printing, regardless of it being at the office or home office. Businesses are going to print stuff. Just because the printing happens from your home doesn't mean it's "home" printing.
They're trying to get Mom to print off her recipe rather than writing it down on a piece of paper. Or get her to send those photos Jimmy just e-mailed from college to her local printer rather than the local Walgreens. And similarly if I can send my grandma a tablet and printer at the same time, with the possibility of them already being configured to work together out of the box, they have a better chance of getting my business than the Samsung folk.
I agree it's a stereotype, and while it may not be "fact", it certainly is far from fiction. HP wants to continue selling their unicorn-blood-laced-ink to the masses, and convert all those that switched to Epson, Canon, or Brother back to them with a better selling point: the integrated platform. You and I aren't their target market with this.