>>14
Language doesn't work like that. If the majority of native speakers think it's natural, then it's natural. If not, the wording is awkward or obsolete.
I know google isn't that reliable, but do you really think it's wrong to say 小学生の時に when you see "Results 1 - 10 of about 1,390,000 for "小学生の時に". (0.07 seconds)"?
Actually it depends on the time span the speaker is picturing in their mind. If you're referring to a moment or an event that happened when you were a grade schooler, you most likely use に, and if your statement is general and relates to a longer time span, maybe you don't say に. I don't think this is a strict rule though.
Anyway, you seem to be very good at Japanese grammar. If anything, better than I am. I wouldn't notice the time space difference if you didn't mention that, even though I'm Japanese lol