(To cover my ***, I'm just suggesting this is safe, not telling you without a doubt that it's safe): if I had left the hard-boiled eggs on the counter overnight, I'd just roll my eyeballs at myself for being absent-minded, and either eat them right away or put them in the fridge as per my intention. Remember, the eggs needed some time to cool to room temperature anyhow, before being put in the fridge. I'd use the refrigerated ones in the next day or two, though, and not leave them for a week!
Mind you, even in this particularly hot summer it never got over 21 C / 70 F in the kitchen (in winter, I put things in the fridge to protect them from possible freezing!). I might answer differently if I knew how hot your kitchen had been while the eggs were left out, and for how long they had been left.