My children have all gone to school.
The first school was terrible for teaching spelling - only thing done to teach was random and confusing weekly spelling list that sap their confidence however hard they tried - and where incorrect spelling weren't pointed out as spelling would emerge.
Current school does teach spelling but via computer s - which research I've read is one of the less efficient ways.
So we've had to step in to teach spelling - fine by DH has long jobs with long hours and commutes and work away a lot - so it's down to me. Me - a person who's spelling is so bad it did finally lead to me going through process and being diagnosed as dyslexic.
Luckily there are lots of very good spelling programs out there - which I've had to fit round school with tired worn out children to correct their poor spelling. So I don't think it's impossible for a poor speller to ensure their own children spell well as the OP seems to be suggesting.
I think spelling wise we'd have worked on it correctly from the start if we'd home schooled and certainly would have picked up problems faster as we'd have seen their work.
While we don't homes school - I'm aware that to the internet just how many good quality resources are out there and in some ares very good home schooling networks - so in many respects I don't think it ever been easier to provide good quality schooling at home.
Not for us though in the end - despite both DH and I having not just degree but post gradate one as well.
I do think finding fault with spelling in an e-mail is an odd way to decide a parent isn't fit to home school - though maybe Op has other reasons to think that.