Psychology can influence your results Sue found she holed more putts with the pin out simply because the hole appeared larger to her visually, which improved her confidence at address.
Your putting tempo matters Gentle putters who let the ball die into the hole may be more affected by the flagstick than aggressive putters, since a firm ball is less likely to be deflected by the pin.
Flagstick width is a factor A narrower flagstick base is less likely to cause a ball to bounce out, so if your course uses thicker pins, pulling the flag may be the safer option.