Metadata > Read Metadata does indeed correctly read date/time values from the metadata. But some gotchas to be aware of:
- For JPEGs and TIFFs, the metadata is always read/written to the .jpg or .tiff file, never from an associated .xmp sidecar.
- For raws, LR reads/writes the .xmp sidecar; if no sidecar is present, it reads from the raw and writes to a sidecar. There is a preference setting to cause LR to write back to the raw as well.
- There are three metadata sections where LR (and other programs) read/writes photo date/time metadata: XMP, EXIF, and IPTC. When writing updated values, LR changes all three sections. When reading, LR examines all three sections, and uses the rules in the Metadata Working Group spec to choose which to use if there are conflicting values. So when you use an external tool to change the metadata date/times, its best to update the date/time in all three, or update one and delete from the other two. I have no idea what Photo Mechanic does, but Exiftool in general does not update all three sections (since the corresponding field may have a different name in each section).
LR provides no way to change DateTimeDigitized -- you'll have to use an external tool or use one of the plugins that let you invoke Exiftool more conveniently from within LR.
One version of LR years ago changed the Edit Capture Time command to also update DateTimeDigitized, but Adobe promptly backed out that ill-considered change in the next release. A fair number of people use LR to also manage scans in which DateTimeDigitized differs from DateTimeOriginal, and the Edit Capture Time was wiping out that carefully entered metadata. I think Adobe figured that almost all users of digital cameras don't really care about DateTimeDigitized since there cameras don't add that field, so it wasn't important for Edit Capture Time to update it.
Of course, it would be better for LR to let you edit it explicitly.