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I was actually checking to see if it was Takeuchi Akari's name on the letter.

Around 2010, Fukuda Kanon (the writer of Ashita Yarou wa Bakayarou) was in a revival group (Shin Mini Moni) with Miyamoto Karin and Takeuchi Akari. Akari has mentioned in interviews that she was really popular in 6th grade (2009-2010(?)) and received many confession letters. Since Kanon was in the H!P eggs she would have been knowledgeable about any egg gossip around this time. What if Karin and Sayuki had both given Akari-senpai confession letters at the same time and then "fought" over it? If that was true then Kanon would have found out about it and it might have made an impression on the song writing part of her brain. So, Kanon might have wrote that part of the song as a reference to Karin and Sayuki. And, Karin and Sayuki might also know about this but be okay with it since they are more grown up now. So, the PV scene might have an extra "edge" because the two have been there before for real.