The first hint is the Sun's timeline. Their report says that the photos show Kim at the prestigious International School of Berne sometime between 1994 and 1997, when he would have been aged 11 to 14. That lines up with what we know about Kim's age (a sushi chef who later defected says Kim's birthday is Jan. 8, 1983), but those are the wrong years for him to be in Switzerland.
As The Washington Post previously reported, Kim is known to have attended Swiss boarding school between 1998 and 2000, when he would have been 15 to 17 years old. Former classmates describe him as living in his own apartment near campus and playing lots of basketball; not the activities you expect of a 12-year-old.
The second problem is the name of the school, which the Sun identifies as the International School of Berne. But Kim is known to have attended the Liebefeld-Steinhölzli Schule, which is near, but not in, Bern.
There's a significant possibility that, assuming those photos are not just of some innocent Korean child, they actually show Kim's older brother, Kim Jong Chol. Both Kims did attend Swiss boarding school, although they went to different schools and at different times. Kim Jong Chol is known to have attended the International School of Berne, the school identified in these photos, and around the time that these photos were taken, which suggests that they may well be of him.
This would not be the first time that school-age Kim Jong Un and Kim Jong Chol were confused for one another. In 2009, when their father Kim Jong Il began setting the stage for a succession after his death, and reporters first unearthed the sons' time abroad, it was not easy to keep the two sorted. Both traveled under false names, lived under false identities, and left suddenly and mysteriously. At the time, their stories were difficult to reliably separate, and one brother was often confused for the other.
Reporters eventually sorted out that Kim Jong Un used the name Pak-un and that Kim Jong Chol used the named Pak-chol (see the parallels?), which made it easier to line up the fake identities with the real ones. The Swiss schools might not have known who their students really were, after all, but they're at least able to confirm the attendance of Pak-un and Pak-chol.
Still, even if the photos are of Kim Jong Chol rather than Kim Jong Un, they are more broadly consistent with the Kim family's apparent, if quiet, love of some aspects of Western culture. Despite cultivating public images as hyper-nationalists resolutely opposed to the imperialist Americans and everything they stand for, members of the Kim family appear to love, for example, American basketball and Eric Clapton. (A third son, Kim Jong Nam, was caught trying to sneak into Disneyland in Japan. He would have been in his mid-20s at the time these photos were taken, and is not believe to have attended a Swiss boarding school, so it's not him.) Fellow students from their time in Switzerland tend to describe them as having fit in with Western peers just fine. So it would not be shocking if one of Kim Jong Il's sons had sung and danced along to a school performance as "Grease." In this case, though, that son was probably not Kim Jong Un.