The problem shouldn't really occur if ATC are involved; they should ensure altitude separation. The situation referred to by the OP is more likely to occur in Class G and then we have to rely on everyone else doing the right thing with regard to choice of flight level....good luck!
If not, the "book" answer assumes that both pilots are aware of the other's aircraft. From experience this most certainly isn't always the case.
Problem comes if you think it's better to go to your left because you're slightly offset to the left of the other aircraft and at that same time he suddenly spots you and breaks hard to his right....you're then on a collision course and you're also in the wrong.
The trick is deciding when you're absolutely head on, or not. Sometimes you look close but are not actually on a collision course and it might then be better to continue straight ahead, or change altitude slightly to avoid. As usual though, in aviation, there isn't a one size fits all answer.