For me, I can get over it and imagine things like that without the need for the game to specifically call it out. There's not a huge difference because the game doesn't specify things like that on purpose. Maybe in one world every wizard spell in some way came from studying what a monster did and how they did it, and then figuring out how to do it yourself. Or maybe we independently came up with some of it.To me there's a huge difference between "I can do something similar" and "that type of monsters all went to school at Wizard-mart" which is what spell-like abillities do. Even the name is backwards - you shouldn't get spell-like abilities so much as ability-like spells that were created to try and fake certain natural abilities.
I can see why you might think the way you do because of the presentation, but out of character it makes for a simpler organization of abilities, and in character humans are human-centric, we compare things to what we know. I could totally see a wizard copying a spell from a beast, and then later his apprentices come across the beast and sees the beast and say "Hey! That beast is copying our master's spell!".
I agree, that's why a lot of abilities describe stuff as "it's this spell, but it has these key differences which probably make it way better or usable at-will".And I find it no more weird to have magical creatures that could use natural affinities and biology for better charming than a human can manage by faking it via spells than I find it weird that a dragon, through its biology and magical affinities can breathe fire in a way no human wizard can manage by faking it via spells. The strength of wizards is versatility, not focus and specialism.