Let me try to remove the nonsense from that and see if I can understand what you're worried about.
Last night you tried to find something on safari using your phone. Your battery was at 30% and you were on 3G rather than LTE.
Later, your battery was at 100%, you were on LTE, and you were able to reach the same site.
Things that aren't relevant: your date, the time(in general), and your battery.
This was a network issue. It could have been at one of many places. You've placed it on two possibilities. The site you were trying to reach may have had server issues or may have just been doing maint as it was later at night.
If you weren't on wifi, which is something to notice before you worry about battery life, the lack of LTE might suggest the towers near you were having issues or the service provider was having issues in their hub.
If you were on wifi, it could have been the same basic problems with your ISP instead of your phone provider. It also could have been an issue with your home network.
Ultimately, there's no such thing as a network with 100% uptime. They simply don't exist. It's never happened before. They fixed it. Who cares who is "at fault?" It'll take you more time to pinpoint the problem by making dozens of phone calls until you find someone who is 1) knowledgeable of the outage and 2) willing to discuss it with someone not in the company than it would to just do what you want to do in the first place.