Reef safe is subjective. To me, reef safe only means that the fish will not harm the sessile invertebrates in my tank. Basically, they should not eat the corals, polyps, etc. Note the "should". That said, I am not aware of a single instance where a Moray has preyed upon a reef. For that matter, groupers, lionfish, scorpion fish, anglers, etc. would all be considered safe for a reef.
There are several reasons that I would be hesitant though:
1. Predators produce a lot of waste, so your husbandry needs to be top notch to keep the parameters in check.
2. Some predators, especially most Morays, get large, are active, and are very very strong. This can cause a few issues ranging from escape from the tank to destroying your aquascape while they move. Some eels will even use rock work for leverage while they tear their prey into smaller parts. If you do not have a tight fitting lid with no gaps, and very secure rock work, do not get a large eel.
3. They are temperamental with diet. Generally zebras, Golden Dwarfs, Chainlinks, etc are not fish eaters, but they can change their minds. You may be fine with proper feeding, and you may not be. It is up to your particular fish and they can change their minds on what they like.
4. Many eels eat crustaceans as part of their natural diet, and these are more likely to get eaten by the three I just mentioned.
5. They can eat something much larger than you think they can, and they can eat a lot in a sitting. If they decide they have a taste for fish, you would be surprised how large of prey they can take... including other eels.
I think that moray eels are amazing to see in a reef though, so if you are aware of what can go wrong, you can have a very successful tank with a large eel. Just stay on top of the husbandry. I just tore down my large DT getting ready to build a new house, but I already have a Dwarf Golden Moray on my list for what I will re-stocking it with when I set it back up in January. I just have to be aware that this means that I may never have small fish or shrimp.
