Ok bear with me here...
Row percentages with in a breakdown seem require the full metric field to be included in order to be calculated across the row. Otherwise it calculates across the entire report.
Why does the system generated percentages not match the calculated percentages?
Within a breakdown, the system generated ROW percentages are actually percentages of the higher level dimension for that specific day.
See screenshots below...
i.e. Reference and Tools breakdown for Sept 1... Aud Non Registered User Page Views shows a ROW percentage of 25.6%. That is NOT 25% of page views on 9/1 within the reference pillar. Its actually shows that the 811K page views are 25.6% of the entire page views for the entire day. (see 2nd screenshot to compare)
811,220 / 0.2561058 = 3,168,828 (This is the total page views across the site for 9/1 NOT for just the parent row)
Non Reg + Reg PV = 811,220 + 841,128 = 1,652,348 - This matches the total page views for the reference pillar for 9/1/20.
I really hope this makes sense...
Below is only 9/1 to show the total PV for the day referenced above.