I would trust them if they are top exchanges but to the point so they can work on it, even though in the background their words don't necessary true and could be worse in the background. I've seen something like if they get hacked and they said "your funds are safe" but in the background it's worse than that so they told us "safe" to keep the users on their platform. You can store small money on there but whatever you do, there are always risks that exchange could have problem later, that risks your money as well.