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Max Max is offline
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Default Counting multiple values (including blanks) in one column

.. It still does not count blanks in column C

This part in the expression should have taken care of it:
..+(C2:C10="")..


Perhaps there are white space(s) in the cells,
these cells might appear "blank" but are not really so.

Try wrapping a TRIM around the range, viz try:
=SUMPRODUCT((A2:A10="Fred")*(B2:B10<"bob")*((C2:C 10="AA")+(TRIM(C2:C10)="")))
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Max
Singapore
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