Not true for all cultivars. For example, the emerald orange rind always looks like a lime.
Limes will actually turn yellow when ripe. We just pick them early.
Sometimes they'll go orange in the rind but most times they stay green like a lime.
Just like with oranges, their skin will remain green or mostly green unless grown where it gets cold enough, then their skin will turn yellow then orange then reddish orange. Where I live, calamondins trees have entirely orange fruit when ripe.
Limes will actually turn yellow when ripe. We just pick them early.