According to wikipedia, "the theoretical risk of a coincidental match is 1 in 100 billion (100,000,000,000) although the practical risk is actually 1 in 1,000 because monozygotic twins are 0.2% of the human population", so it looks like some twins will cause an issue for DNA-based convictions, but I think a non-twin sibling is probably diverse enough? I have different eye colour, ears, food intolerances to my brothers, so I feel like our DNA is pretty different ("pretty" on a scale of human to human comparisons, since 99.9% of DNA is identical between humans or something like that).

I'd argue that while a DNA match could be a very good starting point for a conviction, other evidence should also be presented, for the reasons you suggest. For example, there is the case of the Phantom of Heillbron (https://en.wikipedia.org/wiki/Phantom_of_Heilbronn), where European police found DNA evidence of a woman being at many diverse crime scenes, but it turned out the cotton swabs used for testing were contaminated by at worker at the factory (The swabs weren't certified for police work)