Hmmmm.... after further investigation I've discovered that the time stamp formatting caused the problem. Therefore, I created an additional column and used =INT to remove the time stamp and updated the original formula to reference the cell.
Thanks for listening..
Please explain why my formula does not count some date ranges when data is copied rather than typed manually. In cells K5 and K6 the formula will only calculate correctly when the values are pasted in from Example 2. The same goes for cells M5 and M6. The formatting appears to be the same for all cells.