Actually, she's right. You need higher speed at higher altitudes in
order to maintain a given amount of lift, because the air isn't as
dense. However, you don't necessarily need more power, because thin
air presents a lot less resistance to the aircraft.

You need more power to maintain the same amount of lift as you get higher.
By "same amount of lift" I take that to mean angle of attack and the
resulting IAS for the same dynamic pressure. The formula is predicated on
TAS.