The two storylines are completely separate, and the code for the data disc event doesn't reference Kana's events in any way whatsoever, so that should be impossible. If you send me your latest save file via the CK Discord's #help channel I can look at the variables and fix what's broken.
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Unfortunately I've already since saved over the save file in question after loading up and trying again with an older save.
If it helps though, the Kana event in question was the one where you're woken up and told that she's gone missing (her heat event). Best I can guess, the disk part ended and allowed the Kana event to activate instead of immediately going to the TV part.
Sorry I couldn't be of better help. Didn't think to keep the save.