I got plenty of copyright claims on my YouTube channel from Qanawat Audio because I uploaded videos with Abdullah Al-Juhani's recitations in them. I wonder, were they right in copyrighting my video? For your information, this is my channel: https://www.youtube.com/channel/UCJv0STX-xSkapow54orIJ6g/videos?disable_polymer=1
Of course they can claim your videos if you use their copyrighted material.
Qanawat Audio is some big Arabic publisher and they have rights to many imams and their video and audio broadcasts and recordings. The recitations are simply part of those. As I see, there are many who share Abdullah Al-Juhani's recitations but apparently they do so illegally.
I don't think Abdullah Al-Juhani minds all that sharing, only Qanawat doesn't want you to make money off it.
In short: yes, they can because they have the rights.