I have a similar story to this, I have a friend who is currently here to visit us for the holidays.
She has a Pakistani passport and a U.S. green card, lives in the DC area. AC employees would not let her check in at the airport or online - saying she would be rejected at Canadian customs. They said she could not get the ETA done at the airport - and said she would not be able to do her trip.

Ended up wasting her ticket, flew to Buffalo on new ticket and had no issues coming across the border by land - after someone at the air canada call center said its different rules by land vs air.

She went to Montreal for work in September and had no issues then.

Still not exactly sure what the rules are, the land crossing said she could have flown and would not hAve had any issues.