I did a quick test how FCP 10.6.8 grabs movie dates.
Here are almost all the possible date tags that are deliberately set different (file name does not matter):
exiftool -a -G1 -s -fileOrder5 FileName -api LargeFileSupport=1 -api QuickTimeUTC=1 -Keys:CreationDate -UserData:DateTimeOriginal -QuickTime:CreateDate -System:FileModifyDate -MacOS:FileCreateDate -XMP-exif:DateTimeOriginal .
======== ./movie_m4v.m4v
[Keys] CreationDate : 2005:05:05 12:05:05+02:00
[UserData] DateTimeOriginal : 2004:04:04 12:04:04+02:00
[QuickTime] CreateDate : 2003:03:03 12:03:03+02:00
[System] FileModifyDate : 2002:02:02 12:02:02+02:00
[MacOS] FileCreateDate : 2001:01:01 12:01:01+02:00
[XMP-exif] DateTimeOriginal : 2000:01:01 12:00:00+02:00
======== ./movie_mov.mov
[Keys] CreationDate : 2005:05:05 12:05:05+02:00
[UserData] DateTimeOriginal : 2004:04:04 12:04:04+02:00
[QuickTime] CreateDate : 2003:03:03 12:03:03+02:00
[System] FileModifyDate : 2002:02:02 12:02:02+02:00
[MacOS] FileCreateDate : 2001:01:01 12:01:01+02:00
[XMP-exif] DateTimeOriginal : 2000:01:01 12:00:00+02:00
======== ./movie_mp4.mp4
[Keys] CreationDate : 2005:05:05 12:05:05+02:00
[UserData] DateTimeOriginal : 2004:04:04 12:04:04+02:00
[QuickTime] CreateDate : 2003:03:03 12:03:03+02:00
[System] FileModifyDate : 2002:02:02 12:02:02+02:00
[MacOS] FileCreateDate : 2001:01:01 12:01:01+02:00
[XMP-exif] DateTimeOriginal : 2000:01:01 12:00:00+02:00
FCP import dialog always shows MacOS:FileCreateDate (it is not an internal metadata date but that fragile system date that can very easily change when moving files around):

But on the other hand, FCP browser then shows Keys:CreationDate (the time is +1 hour incorrect because FCP seems to use computer timezone and also add DST to it):

If Keys:CreationDate is removed, then FCP grabs the date from QuickTime:CreateDate to .m4v and from MacOS:FileCreateDate to .mp4 and .mov:

Finally, if QuickTime:CreateDate is zeroed, FCP gets all those dates from MacOS:FileCreateDate:
exiftool -a -G1 -s -fileOrder5 FileName -api LargeFileSupport=1 -api QuickTimeUTC=0 -Keys:CreationDate -UserData:DateTimeOriginal -QuickTime:CreateDate -System:FileModifyDate -MacOS:FileCreateDate -XMP-exif:DateTimeOriginal .
======== ./movie_m4v.m4v
[QuickTime] CreateDate : 0000:00:00 00:00:00
[System] FileModifyDate : 2002:02:02 12:02:02+02:00
[MacOS] FileCreateDate : 2001:01:01 12:01:01+02:00
======== ./movie_mov.mov
[QuickTime] CreateDate : 0000:00:00 00:00:00
[System] FileModifyDate : 2002:02:02 12:02:02+02:00
[MacOS] FileCreateDate : 2001:01:01 12:01:01+02:00
======== ./movie_mp4.mp4
[QuickTime] CreateDate : 0000:00:00 00:00:00
[System] FileModifyDate : 2002:02:02 12:02:02+02:00
[MacOS] FileCreateDate : 2001:01:01 12:01:01+02:00

I usually do not pay attention to those dates because I have the date in the filename as 2006-0606-1206-06.mp4