I don't see news or articles about people being robbed in Bitcoin transactions very often, but that risk is always present.
Last year there was a flood wave of news articles about people who got robbed off their coins or cash. I'm sure that most cases don't even make it to the news because the amounts concerned are too small. Don't forget, the higher the price is, the more incentive criminals have to chase after local buyers and sellers of coins. Risk increases day by day.
I think 1 confirmation is enough to say that your Bitcoin is coming to your wallet, there will be no cancellation since it's already approved and put to the chain. You just need to wait miners to confirm your transactions and then your will received it on your wallet.
Stale blocks are somewhat of a risk though, so there is no absoluteness when your transaction has only 1 confirmation. If the transaction value is on the lower side, there isn't much to worry about, but when you're dealing with large value transfers, definitely make sure to pocket that second confirmation before you walk away.