I don't necessarily think that naproxen and aspirin are dangerous, as long as the maximum amount of pain reliever that can be taken in a day is not surpassed.
Both naproxen and aspirin are non-steroidal anti-inflammatory drugs. This category of drugs is known for affecting the gastro-intestinal system and increasing the risk of stomach ulcers. So if you were to take both drugs in the same day, in the dosages allowed for on the label, you will have taken twice the amount of NSAID medications you can possibly take in 24 hours. Of course, this is dangerous.
If you were to talk half dose of each however, making sure not to surpass the maximum dosage, it's probably not going to cause an issue. Of course, if someone is taking other medications as well, or has a very sensitive stomach, they can't combine these at all.
I don't want anyone to go by my advice though because I'm not a doctor and everyone reacts differently to drugs. Always ask your physician or pharmacist before mixing drugs.