Missing trophy timestamps on PS4

I never play online on my PS4. As I'm sure many of you know, missing timestamps are perfectly normal on PS3s and Vitas that are only played offline. But on PS4 they are tied to the internal clock even if you've never connected it online. After updating to 7.02 however, trophies started showing up with missing timestamps.

I like to look back at my old trophies and see when I got them so this irritates me. Anyone else had this problem? I tried searching for answers but it seems on PS4 this is a rare anomaly.

I'm pretty sure it's not the clock being dead, because it doesn't ask me to set it every time the PS4 has been unplugged for a while.

I've got nothing, I never realized they were time-stamped.

Ah, well I hope someone knows what exactly is causing this and if it can be fixed. Maybe the problem is rare because it gets fixed once you go online and sync? I imagine 90% of PS4 players use online these days.

But it is very strange that this is an issue at all considering the normal/visible clock that you can set manually still seems to work fine. Is it just the invisible/internal one that is broken somehow? Offline PS4s have been keeping track of trophies for years with no issues until recently. At least as far as I know.

I just realized that the first trophy I earned on my Vita from Welcome Park never had a time stamp since I earned it before linking it to my PSN account. Is there any way to retroactively get a time stamp for this trophy?