Hardware was part of the service, obviously.

It is very misleading or outright perverse to write "they were selling software as a service in the IBM 360 days" when there was no network that could be used to the deliver the service to the customer and when the service was available only to purchasers of hardware that started at $655,000 (2025 dollars).

Also, IIRC the software consisted mainly or entirely of systems software, meaning that almost all customers had to employ programmers to make effective use of the "software as a service".