The suggestion first seems to have appeared in diving literature in the early 1970's. It was referenced as a guideline to follow in order to reduce or eliminate the need for decompression stops. For example, diving first to 100ft for 20 minutes then to 40ft for 60 minutes with a surface interval of 1 hour you do not need to complete any decompression stops, but if you dive in reverse, starting with the 40 ft dive followed by the 100 ft dive, you need 2 decompression stops for a total of 26 minutes.
The reference never provides any hard evidence that not following the rule will be detrimental to your health.
The AAUS (American Academy of Underwater Sciences) decided to look into this matter further to see if there was sufficient evidence to create an actual diving rule. They looked at current practices and diving risks associated with diving in reverse. The conclusion was that as long as a diver is being safe and working to avoid decompression dives and the injuries associated with decompression sickness there is no need to follow the deepest dive first guideline as though it were a rule.
This doesnt mean toss out everything you know, it simply means, if you find yourself doing a deep dive after you have done a shallow one, more than likely, nothing will happen to you as long as you stay within your limits.