It's been awhile, but I have been pulled aside by both US Customs and Canadian Customs when trying to enter the country using only my Nexus card. I recall being told that it is an acceptable form of ID and does make cross the borders easier for both traveler and customs agents, but I was told both times. "You should travel with your Passport and your Nexus Card". I was only ever hassled, never denied boarding.
From the GOES website:
Benefits
Expedited vehicle/pedestrian entrance into U.S. or Canada.
Expedited marine entry into U.S. from Canada.
Access to TSA PreCheck® expedited security lanes at airports within the U.S. and U.S territories for U.S. Citizens, U.S. lawful permanent residents and Canadian citizens.
None of the benefits listed are "replaces passport". Yes you can dig into the Western Hemisphere Travel Initiative and find somewhere that US Citizens can cross with just Nexus.
What the Canadian Border Services Website says is:Citizens of the U.S. who are members of the NEXUS program may present their membership card as proof of identification and as a document that denotes citizenship, when arriving by air (when coming from the U.S.), land, or marine modes.
Citizens of the U.S. who are members of the FAST program may use their cards as proof of identity when arriving by land and marine modes only.
Permanent residents of the U.S. who are members of the NEXUS or FAST programs must travel with a passport and proof of permanent residence, and may be asked to present these documents to the officer upon arrival at the border.
But Canadian Border Services also lists documentation that you should carry with you about "legal custody of minors". Usually this only happens when flying solo with a child or parents with different surnames, but if there is something the gate agent didn't like about your daughter not carrying a passport, while the two of you did - all it has to do is raise a red flag - especially when it comes to crossing borders with small Children.
And just because you had a compliant CSB agent in Vancouver at the land border, doesn't mean you would have had one when landing at YVR.
Sorry you may be in the "right" on paper/websites, but AC is going to have all kinds "out clauses" for why the agent had the "right" to refuse you boarding. (and refuse is different than denied - denied comes with compensation - refused does not). My guess is you were refused boarding because of inconsistent travel documents travelling with a minor. And remember AC did this at great cost to themselves (deplaning passengers and luggage is not cheap) - it would have been far easier for them to let you on.
You may have been in the right and could have gotten away with it, and I would have been pissed too, but I think you have an uphill battle with an airline that is going to support a "safety call" by an agent at the gate.