I don't think that's the problem the clarification is designed to address. A plover is a type of bird, and in some accents it doesn't rhyme with either lover or hover.
Nevertheless, the parent is right, in my accent hover and lover don't rhyme either. All three have different vowels.
In my accent, lover, hover and clover have three different vowels in the first syllable. Plover rhymes with lover for me. Does it rhyme with clover for you?
I suspect it's not the standard pronunciation in my region, since Wiktionary lists it as an alternative American pronunciation and I'm Australian, but for whatever reason that's how I pronounce it.
I expect that many people pronounce "plover" as "clover" if they saw it written down first before they heard someone who knows the pronunciation say it. There are plenty of words like that in English.
I pronounced it as rhyming with "clover" too before learning that it's actually incorrect.
Nevertheless, the parent is right, in my accent hover and lover don't rhyme either. All three have different vowels.