You just found another bug.
The reason why DateTime is displayed is this line of code:
if (strpos($showExifStr,"|".$key) !== false && isset($val)){
(original version is without without my "!==" hack, ofc)
Since that line only looks for the start of $key (i.e. "DateTime"), it will evaluate as true when it finds "DateTimeOriginal" or "DateTimedigitized" in $showExifStr, even though the key "DateTime" isn't even in $showExifStr.
Why DateTime isn't selectable in exifmgr.php I don't know (haven't looked into it), but it is a valid EXIF tag (at least in my camera), and hence should be selectable as an option in exifmgr.php, IMO. But as I said, I haven't looked into that matter so there may be a reason for it. Maybe a developer have a fast answer?
<Edit>
It seems it's as easy as this: if you want to be able to choose DateTime, just add it to $exif_info in exifmgr.php and in exif_php.inc.php. I.e., if you want to display DateTime between AFFocusPosition and Adapter you just change
$exif_info = "AFFocusPosition|Adapter|...";
to
$exif_info = "AFFocusPosition|DateTime|Adapter|...";
Remember to do it in both files, and to go to exifmgr.php and review your checkboxes as they will be bumped out of order if you put DateTime anywhere else but last in $exif_info.
</Edit>
I have a working version of a new exif_php.inc.php where I replace $showExifStr with an array instead, to be able to do a real comparison between what's in the $exif array and what should be shown. It works but has a few unsorted issues so far, I will post here when it's done.