Yes, Upgrade you can double hop. 9.1 -> 9.3 -> 9.5 -> 9.7
Downgrade is typically more granular and is disruptive and a very last resort typically done at the direction of Support.
You mean this line? "Note:Please note that direct revert from ONTAP 9.7P8 to ONTAP 9.3P17 is not allowed. You must perform a revert from 9.7P8 to9.6P9". I think it's just saying you can't go directly, i've not ever seen a UA spell out every step in a downgrade. Or, (speculation here) there is something specific to that model of controller where system firmware hadn't changed between 9.3 and 9.6. highly unlikely though.
Support is typically engaged before doing so. I think i've only reverted a cluster 1 time in the last 6+ years. And i've not ever done the "direct" 9.3 to 9.7 upgrade because customers always wanted to verify between major versions.