I don't think there's any possibility that right on both accounts could ever be uttered by a native speaker who also knew right on both counts and considered that to have a different meaning.
I'm inclined to interpret this NGram as evidence of an increasing number in recent decades (but still a tiny minority) who've misheard or misremembered the normal usage...
...but I do acknowledge that there's a strong historical/etymological connection between count and account here. OED's closest definition is...
5b: the act or way of estimating or regarding; estimate, regard, notice, note; = account n. IV.;
esp. in phr. to take, make, set (no) count of (upon, by) . arch.
But I'd set more count/account by this Merriam-Webster definition...
3a: allegation, charge; specifically : one separately stating the cause of action or prosecution in a legal declaration or indictment (e.g. - "guilty on all counts")
3b: a specific point under consideration : issue
(For the specific usage under consideration here, that last highlighted definition applies! :)