The human body is an adaptive organism. It will attempt to acclimate to any given circumstance, in order to bring about stability within its own environment. Once it achieves this, the body will seek to maintain the status quo, till further need for change is called for.
If we do not expose the body to a training stressor, it will adapt to the lifestyle of sedentary activity.
Training three days a week from none at all, will force the body to adapt to a three-day training week. If we believe and expect the body to only tolerate a three-day training week, it will adapt to exactly that.
If we push it from three days to six days per week, the body will strive to adapt to the increased stressor in training frequency.
Overtraining can only take place if (and that is a big if) the body cannot recover in time for the proceeding workout. Factors such as undernourishment, rest and hydration must be closely monitored, as they have a significant role to play in the process.
Providing all of the above factors remain constant and in check, overtraining is very hard to achieve, as the body is constantly striving to adapt to the training stressor.