Another possible scenario is if you use the 'Print Invoices' function to print a range of invoices. After the invoices have been sent to the printer, a screen appears that asks if 'Everything printed OK', with a choice of Yes or No. The Print status of the invoices (or any other document, including picking lists) are not set until Yes is selected here.
If you have a second person also printing a range of invoices in OrderEntry, and they select a range that overlaps what another person printed, all invoices without the Print status set will be printed. Because the first person may not have identified that invoices have printed successfully, the print status may not have been set yet.
The solution here is to have people who print a range of invoices (or other documents) to click Yes before another person attempts to print. This may mean clicking Yes as soon as they print, but this is a decision up to you to make.
Note that all of this above is not related to the setting to 'Reprint invoices already printed'.