It's very common, and generally quite safe. Both the computer systems in air traffic control and the traffic avoidance systems on the individual aircraft are able to handle it nicely.

The article mentions the Embraer's TCAS alerted them of the problem, for example. Even my dad's little four seater prop plane will call out "traffic, twelve o'clock, three miles" sort of notices, and if the traffic gets too close it can additionally order climb/descent to avoid.

Vertical separation (based on altimeters) is way more precise than horizontal separation (based on radar, VHF navigation, GPS, eyeballs, etc).