Logs on the website of geocaching.com will be displayed in the time zone of Seattle (PST). When you create a log from another time zone the date displayed on the GC website can be on another day.
An example: This is the case when you create a log from Germany (GMT+1) before 08:00 AM.
If L4C would correct the log times automaticly by your timezone, then the log would be displayed proper on the GC website. But the data in the database would be wrong. This data is provided to other apps and programs by the Live API and by gpx files. How the target program displays the dates depends on how this program works with time zones.
Because it is probable that the GC website will be extended to display the dates in other time zones, I think it´s correct to submit the real time to GC out of L4C.
You have the possiblity to adjust the log time by yourself. So you have the chance to modify the time if you want it (like if you log a cache before 8 AM in Germany). You can decide if you want the log in the proper date on the GC website or if you wan´t them correct in thier database (and so also in the most other programs and apps).