Why do iPhone photos have Microsoft in Exif data? Wandering around Spain, I took a lot of pictures with an iPhone 5s, latest IOS. 

Uploaded into the new Photos (which is IMHO a step backward from iPhoto).

Dragged from Photos into a directory, and viewed tags with exiftool.  Puzzled by this one in every image:

Primary Platform                : Microsoft Corporation


What does it mean/why is it in images that came from an iPhone and (AFAIK) has not been created by, stored on, or passed through any software or hardware from Microsoft?

Again, I took all these photos with an iPhone 5s and all changes (if any) were made by Apple's new but not improved Photos app.
"Primary Platform" is part of the ICC profile, which is related to colorspace. Under "Device Model" and "Colorspace", you should see sRGB, which was created jointly by Microsoft and Hewlett-Packard (HP). If you look further you should also see the color profile is listed as being created by, and copyrighted to, HP.

It appears that somewhere along the line, the color profile is being added to the image. It's not clear if this is on iOS (which I've seen claims stating it is not color-managed), during the move to Mac or in iPhoto/Photos. I have images that were in iPhoto and copied back out, and have not been touched by Photos, that have the same Exif data. I have also used the Photo Investigator app on iPhone to view Exif data for images that were taken on iPhone but have not yet been transferred to a computer, and they list the Color Model as RGB, not sRGB, so it would appear the profile is added later.