Vista Home Basic does run on the Intel 915 chipset.
Intel decided not to bother producing a WDDM video driver for the chipset, probably because they felt it wouldn't perform well enough to be worth the effort.
Therefore the Aero interface doesn't work.
Windows Vista Home Basic doesn't even include Aero.
Ummm, no.
Intel produced a WDDM video driver for Vista. Then Microsoft changed the spec and refused to certify it.
Bait and switch.