If the teacher made the expectation known at the beginning of the year that she considers it "incorrect" to capitalize common nouns, then it isn't being nitpicky. If it was an oversight in her teaching, then she ought to let this incident pass, inform the students of the "rules", and from that point forward the children would be expected to follow that rule.
Maybe you can find out if that expectation was made clear to the children. Technically, it is an error to spell common nouns with a capital letter at the beginning. For some reason, my kids have always been taught and have understood that standard, and they aren't in a special school for smart kids.
The other thing you can do is let Rhys know about this "rule" yourself, and have him consider it a learning experience. I wouldn't think it would be worth the trouble to make an issue of it with the teacher, regardless of whether I thought the teacher was being nitpicky or not.
As well, I'm sure Rhys has a spelling text book that the teacher uses to give the assignment, or if she prepares the spelling words herself, have a look at the page where the spelling is modelled for the children. All of the spelling words, when tested, should be spelled by the students exactly the same as what is modelled on the sample pages. If the samples and models are capitalized, how can the teacher expect any different? Just remind Rhys to print the words exactly as they appear in the spelling list.