The German umlaut also comes from small e superscripts over A, O, and U, so while the sentence is technically wrong I do think it’s fair to identify the Swedish Ä and German Ä as the same, conceptually.
If anything, there's a dialectal glide from Ä to E in some places, so we think those two vowels have way more in common than Ä and A.
If you write E instead of A in a word, we can read it, but you look like a small child who hasn't learned proper spelling yet.
If you write Ä instead of A in a word, we're confused, and you look like a foreigner who's learning Swedish and is still confused about the extra vowels.