score:3
It just means that she was denied entry that time for failure to overcome the presumption of immigrant intent. INA 212(a)(7)(A)(i)(I) says you are inadmissible as an immigrant if you don't have an immigrant visa. The logic of why immigrant intent leads to this inadmissibility is kind of indirect -- she was seeking entry as a nonimmigrant (a visitor), but since she failed to overcome the presumption of immigrant intent, the law "presumes" she was an immigrant, and then says she couldn't enter because she didn't have an immigrant visa (which she obviously wouldn't have since she was seeking to enter as a nonimmigrant).
Failure to overcome the presumption of immigrant intent is the most common, generic reason officers use to deny visas or deny entry to nonimmigrants when there's anything they don't like about the person's case or situation. Whether someone convinces the officer that they have no immigrant intent or not is primarily subjective, and any negative factor in the person's case can make it harder for the officer to be convinced. For people applying for visas, they usually get denied at the visa stage under INA 214(b). But Canadians don't need visas to visit the US, so they can only be denied at entry, and when denied at entry for immigrant intent, they give the code INA 212(a)(7)(A)(i)(I).
Inadmissibility on INA 212(a)(7)(A)(i)(I) applies only to a particular entry. Unlike some other inadmissibilities that say one is inadmissible for a period of time or permanently, i.e. you have a "ban", this inadmissibility just means you were inadmissible that particular time. It doesn't mean you will be inadmissible the next time. However, there is a ban that might be triggered when someone is denied entry for this reason, INA 212(a)(9)(A)(i).
When someone is denied entry to the US, one of two things happen: 1) they are allowed to withdraw their application for admission and voluntarily deport, or 2) they are removed. (Though if she was entering at a preclearance facility like a Canadian airport, I don't think she can be removed since she is not in the US, so I believe #2 above doesn't apply.) Whether to allow someone to withdraw their application and voluntarily depart is at the discretion of the officer -- the officer doesn't have to allow it even if the person offers to voluntarily depart. If the person is "removed", that automatically triggers a 5-year ban under INA 212(a)(9)(A)(i). If they are allowed to withdraw their application and voluntarily depart, they do not trigger a ban. In your girlfriend's case, we know she was allowed to withdraw her application and voluntarily depart, so she does not have this ban.
Just because she has no ban doesn't mean they will let her into the US. They could still deny her entry for immigrant intent, or they could let her in for a shorter time, or otherwise subject her to extra scrutiny. The record of her denied entry, and whatever notes they put into the system that time, is seen when she later seeks to enter and is probably causing her to be placed in secondary. There is not much she can really do about this. This is not a ban; so there is no "waiver" to file. It is just individual immigration officers (probably different officers each time), deciding to subject her to extra checks based on her history, which is in their discretion. If she immigrates to the US, then she would probably no longer be scrutinized for this reason.