That's no mere claim. There are a couple time-lapse films allegedly showing 24h sun that were proven to be fakes. Why fake it if it exists? Just do a real video.
They were not actually fake. In the most popular one, it was footage of the Sun going over 360 degrees around, where the last few degrees just started from the beginning again, so it was a loop.
Now what FEers should do is not "debunk" the looped 360th degree, but focus on the other 359 degrees instead. Because that's 24h already.
Here's a totally different video:
And here's a 360° version of it (pan to look around):
I mean, you can keep denying it, because it's easier for you FE folks if you don't have to explain it, but an explanation for Sun on the complete ice ring would still be quite interesting to hear.