When an invisible character leaves a blindsight creature’s reach, does the creature get an Opportunity Attack?

A character in the party cast Invisibility on herself, making her invisible. She then tried to move past a Giant Spider, which has Blindsight 10 ft. Per “Does Blindsight detect Invisibility?” the Spider can still tell that the character was there, since the rules for Blindsight say “A monster with blindsight can perceive its surroundings without relying on sight”

But, as she leaves the Spider’s reach, does the Spider get an Opportunity Attack? Per the rules, “You can make an opportunity attack when a hostile creature that you can see moves out of your reach.”

Blindsight just says “can perceive”, but an Opportunity Attack requires “you can see”. Is the “perceiving” of Blindsight enough to be able to “see” for the purposes of the Opportunity Attack rule?

As the DM, I ruled “no” simply on the principle that “When in doubt, rule in favor of the players”, but I’m really not sure that’s right, as I may be taking things too literally.