You really need to isolate where you are fretting and what fret buzzes. ie: if you fret the first fret and play a note on the bass E string, does it buzz on the second fret? The 3rd? The 12th? While still testing on that first fret, does it buzz on every string? On the same or different frets? Some experimentation will give you the 'lay of the land'.
At the very least, it will cost you nothing to try a small turn on the truss rod. Try releasing tension (counter clockwise) about 1/8 turn. Try that out for a while. Leave it a few hours (I like to leave it a few days) before deciding if another 1/8 turn might be necessary.
When you do this, it's likely to raise the action as well, so you might want to bring the bridge down a bit.
Some general Fender specs are - while capoed at the first fret-
fret at the 22nd (or 21st whatever your last fret is). You should be looking at about .012 neck relief when measured at the 7th fret. Many players go way lower than this, but this is factory settings according to Dale Erlewin.
(Capoing the first fret and fretting the 22nd eliminates the nut and bridge from the equation.)
Once you get the relief settled, string height of the Treble E at the 17th should be about 1/8" (still capod on the first, but don't hold the string down at the 22nd). Adjust the bridge until you get it right. You will want an extra 1/32 or so on the Bass E side and then blend that difference across the strings.
Factory specs are pretty high in my opinion. If you still have fret buzz at this point, you should probably have a tech check it out, but it costs you nothing to try this at least.
Also try another set of strings. They do make duds from time to time.
Please note: I am not a guitar tech, just an enthusiastic player & builder. :)
Good luck!!
...so ever since then, I always hang on to the buckle.