I have literally never seen this before. This is as basic as it gets and you have to think if this was an endemic problem, someone would have commented before.
Therefore I think there has to be something specific to this spreadsheet.
I am able to get something similar to what you have by setting conditional formatting on the cells to suppress values less than 10,000 (or, more specifically, set the cells to show '$0.00' if their inherent value is less than 10,000):

In this way I can set values in cells B3:B9 that are less than $10,000 and they don't show. However, the cell still has that actual, underlying value, and that is what SUM() uses, not the displayed value. This is true of every spreadsheet since, like, forever.
So the question is what values are actually in cells B3:B9? If you click on the cell, what does the formula behind that cell say? What does the window footer say (where it shows values for selected cells).
Moreover, what is it you want these cells to do? If you want them to actually report $0.00, then you need a formula that returns that, rather than just suppressing the display format.