There is nothing particularly special about a perfect match, except that it means that there is more of a chance of finding the common ancestor earlier.
The TMRCA calculation just gives you the odds of finding the common ancestor by a certain number of generations, but it is not precise enough to distinguish the actual number of generations because of the overlap. For example, the ranges for various close matches are:
0.5-8.0 generations for a 67/67 match 1.5-12.0 generations for a 66/67 match 3.0-15.5 generations for a 65/67 match 5.0-18.5 generations for a 64/67 match
Questions 23=27 on the following page show how to interpret results: