I actually personally know a number of drone operators and its not a "just push a button" type scenario. Weapons release requires a significant amount of authorization, ranging from commanders in the field to lawyers in the pentagon. There is up to a dozen people in the chain of command that are all required to say "yes" to engage targets.
The reason they have the luxury is because it is a drone and not a pilot over enemy territory (this is in operations that occur in "areas" not recognized, where the country letting them do the drone strikes doesn't particularly want it known to their general population). A fighter pilot has a lot more stress, and they are more prone to making bad decisions because of the many more immediate constraints on their judgment.
Do drones allow these types of attacks to occur more easily? Probably, but on the other hand they'd probably be executed in some form or fashion either way (cruise missile strikes, which are far more prone to failure in target selection, or human operations, aka spec-ops or hired guns/foreign service).