The white balance data is not stored as a temp and tint in an image. It is a set of data that needs to be interpreted. Different image readers will interpret it slightly differently.
Since ExifTool is giving similar results as Lightroom in the interpretation, LR is probably getting it right.
What are the results you get if you use the latest version of Nikon View NX-i ?
Exiftool correctly reports the WB to be 'Flash' not a numeric colour temp. Nikon Capture NX-D also correctly reads the colour temp as 'Flash'. Not the end of the world, just adds another step to workflow remembering to reset colour temp in LR.
Actually, I can't think of a single instance where I would "trust" the camera white balance. To me, it goes without saying that it always needs to be tweaked a little - even if it was "accurate".
But that's me.
For high accuracy you'd always include a color checker chart, and white balance that.
I use a grey card as well as a colour checker, I'd never trust the camera WB either, that isn't the point though.