Embed date/time stamp on video?

While this isn't a one-click option in Premiere, the following may be a good workaround for you.
Step 1: For your video capture, before you record, set your camera to free-run, time-of-day timecode & sync it up with a clock (that is, if it is 10AM set your camera to 10:00:00:00, if it is 2PM - 14:00:00:00). That way, the timecode in your clips will accurately reflect when it was recorded in 24-hour time.
Step 2: Import your footage into Premiere, and manually enter the date of recording into the "Description" field in your project bin.
Step 3: Add an adjustment layer on top of your footage in the timeline. Apply the "Metadata & Timecode Burn-in" effect. Set "Line 1" to display Source Timecode. That is your accurate "24-hour" time. Set "Line 2" to display Description. This will display the date you have manually entered into the Description box in your bin. Make sure both lines have Source Track set to Top Clip (that is the default behavior).

Legally, I don't know if that is an acceptable solution, since it can absolutely be faked. If you need the metadata indellibly burned-in to the footage you will have to do so at the source -- most if not all cameras have an option to burn-in metadata (date & time) such that it cannot be removed.

Good luck!

I'm sorry to say that this is not a feature available in Premiere. IThe date/time stamp is usually recorded with the hardware that shot the video.