She’s misunderstanding the argument. The margin of error refers to the difference in voting totals for both candidates, not just Bernie Sanders or Hillary Clinton alone. If the polls were just accounting for Sanders out of 100% and not two candidates, then it would be within the margin of error, but since it’s calculating for both, they are outside the margin of error.

For instance, in Ohio, if Sanders and Clinton were 2.5% off each (5% total), then the poll would be roughly within the margin of error. However, since each candidate is about 5% off (10% total), it is 5.2% off the margin of error when taking both into consideration. The table notes this is in the 3rd footnote, using a study to calculate the margin of error at a 95% confidence level.

But thank you for bringing this up; I hope I addressed your and your friend’s concern.