It’s definitely true that brown eyes are dominant.
I think what people are confused about is what dominant actually means.
(there are more than 1 set of genes at play with eye colour, but for simplicity sake, we’ll go with)
you receive one eye gene from mum and one from dad.
If mum and dad both give blue genes, you’ll get blue eyes. Same if both give brown, you’ll have brown.
Now, if mum gives a blue gene, and dad gives a brown gene, you’ll have brown eyes. Because brown is dominant over blue. That’s what dominant means. When both are present, the ‘dominant’ colour shows.
It’s absolutely nothing to do with which gene you then pass on though.
So, when you go on to have your own child, the dominant gene and recessive gene are just as likely to be passed on as each other. I.e. you’re equally likely to give a blue gene as you are a brown one.
its quite common for dark eyed parents to have light eyed children, because they are passing on their recessive gene, whose colour has been ‘overshadowed’ in their own eyes due to also having the dominant gene.
it’s much, much less common for two blue eyed parents to have a dark eyed child (i was actually taught in school it was impossible, but turns out it is possible but just really rare, die there being many sets of genes involved, not just the one)