A Clustrmaps comment excerpt follows below; the company also generously upgraded my account to their + account at no charge. I appreciate the feedback and gesture.
It is crucial to appreciate that in this case there are no "right" or "wrong" numbers, merely different interpretations and counting methods. Our counts are very accurate, and based on industry-standard Apache log files, which provide all the details necessary to compute the results (with no personally identifiable information!). The idea of a restricted time window (normally defined as a 'session') is common in the web analytics industry, but the definition of that window varies for different purposes, and is arbitrary.
There is a great discussion of the problem, along with a nice illustration, in a Wikipedia article on Web Analytics, particularly the section entitled The Hotel Problem.
As mentioned at the beginning, we also have very different aims, namely to provide
a) a 'visual gestalt' overview
b) a 'badge of pride' that you can show off simply on your site (the thumbnail map), with no further explanation
c) city-level detail (all those dots)
d) very rapid map deployment (large maps are all pre-stored for speed)
e) massive scalability (we can show millions of dots instantly, although we appreciate you may not need such numbers, it is nice to know that the capability is there).