@MikeSynnott I haven’t done the digging that you have, and I’m a bit of a layman in regards to some of this low-level stuff, but if it helps to support your theory, I can confirm I’ve been having the exact same issue when trying to program my blinks with an old Acer Netbook (running Windows XP) that I’ve used for some projects in the past. It too does not have any COM ports, and the “Port” menu in the Arduino IDE stays greyed out.
EDIT: I should mention that I haven’t tried @jbobrow’s suggestion of using the Adafruit modified driver for the USBtinyISP. I might give that a try myself when I get home.