When you include the "Total Area" column on your report, you end up getting one row per Precursor Result.
The "Count" operation in the Pivot Editor tells you the number of rows that did not have a blank value in that column. It does not do anything smart, such as figuring out how many of those values are identical to each other.
For this reason, that "Count of Peptide" column ends up being the number of precursors under the protein, which is slightly higher than the number of peptides since some of your peptides have more than one charge state.
I think if you really started with a report that only had the following columns:
and did the pivoting, you would end up with "Count of Peptide" being the correct number. But, if that starting report has any precursor columns (e.g. "Total Area") it will end up throwing off the final count.
If you wanted to use "Total Area", you could still do it. In this case, you would start with a report with the following columns:
and then pivot it, with "Protein", "Peptide", and "Replicate" as Row Headers, and Sum of Total Area as the value.
Then, you would pivot it again, with "Protein" and "Replicate" as Row Headers, and "Count of Peptide" and "Sum of Sum Of Total Area" as values.