What you're describing would most likely fall into an argument of whether the inclusion of the copyrighted music is "fair use." Here's some good analysis from https://www.copyright.com/blog/music-licensing-fair-use/
What is ‘incidental use’? Is that considered fair use?
Pretend you’re a documentary filmmaker, and music is playing in the background at an event you’re covering. When you’re running your camera and you pick up copyrighted music, do you need a license?
As with many rights clearance questions, this often requires a risk assessment.
There are certainly people who argue – and there are credible arguments to be made – that the incidental picking up of the music in the background during a documentary film can qualify for fair use. When you’re talking about incidental music picked up, you’re more likely to qualify for fair use if you’re not focusing on that music, it plays for a short period, and it’s in the background.
If the risk seems too high (for example, how prominent the song is, or how long it’s audible in the video), filmmakers can consider alternatives. These could include blurring out any copyrighted materials by removing the audio sound for any unlicensed music that is picked up.
With that said, I'm not entirely sure what you're asking by your question:
Would Kurtis Mantronik, Harry Styles, Soul II Soul, Taylor Swift or any of their record labels have any case to clame Antonia's hypotheticla video ...
Would they have grounds to file a copyright claim against, let's say YouTube, demanding the video be removed? Sure, they could file a copyright claim, and it might get the video taken down until your girlfriend convinces YouTube that it is indeed fair use. (Offhand, I don't know if YouTube makes those determinations, or if they just say "we're not getting involved, the video will remain removed, you two go to court and let us know who wins.")
Would they have grounds to own your girlfriend's video (if that's what you meant by "claiming" the video)? That seems unlikely: a copyright infringement claim is going to seek a court order that the video be no longer published, your girlfriend turn over any money she made using the copyrighted materials, and money for other reasons, but she'll still "own" the video.