Is the HP Support Assistant "set restore points" the actual method used by Microsoft or an additional option? Thank you.
No.
First off, I have an HP Pavilion Desktop (500-075) purchased 12/2014 so I have some first hand experience. It was preloaded with 8.0 and upgraded to 8.1 and all the other current updates.
IMHO, HP Support Assistant can be a problematic program. ( I will get to that later.)
I don't believe MS uses the HP Framework for any of the MS service routines. If I were you I would turn off all the HP tune-up tasks because they would be redundant, the MS maintenance tasks do everything and more. Anything HP Support Assistant does can be easily performed manually as well. Personally I don't want the HP setting Restore Points and especially defragging the disks. It seems every add-on third party program wants to service your computer. While windows will automatically create some Restore Points under certain conditions I prefer to create them manually so it's always under my control. At any time you can see all the stored Restore Points as well as set the overall storage space for Restore Points by going to the Recovery Section and select Restore Point configuration.
Back to HP Support Assistant: Support Assistant is a rather complex piece of software that I wish was never installed. Check out the HP Support Forum, many HP users have difficulty uninstalling the program and/or getting the proper version to work correctly. I have disabled all the Support Assistant tasks in Task Manager because a couple of the HP service tasks were generating critical errors when attempting to run automatically. Even after all the MS 8.0/8.1 Upgrades and Updates the only real problems I have had were related to HP Support Assistant not any of the MS Upgrades/Updates. I will eventually uninstall the HP Support Assistant but for now, with most functions disabled it is not causing me any issues.