Sorry for the delay in replying. I have been trying to find a simple solution, but it's actually, we'll potentially a far more complicated problem than may first appear!
There are lots a variables, BD/DVD player, TV and then the actual DVDs themselves.
Some early DVDs and a good number of Region 1 DVDs don't have 16:9 auto switching codes. Most of the world outside Europe didn't have a need because the standard phono video connection doesn't detect widescreen like the Scart did! You had to manually select 16:9, Wide, Zoom or as appropriate! What a pain!
The TV situation arises when the set has an overscan mode. Our Panasonic 37in LCD does have this, and we find we have to alter this setting to suit individual sources! Even SkyHD without overscan on, has a black bar all around the image! (Scratch head in dismay)!
This may not be your exact problem though - it just highlights a range of possible issues!
Another situation is when there is a 16:9 image that sits inside a 4:3 window with large black bars all around. On the Panasonic, we usually use Zoom 2 (it does suggest this in the manual).
I don't wish to pry, but could you let me know what TV you have and some example DVDs where the problem you refer to occurs?
We may have had the exact same problem and found a way around it!?
By the way, we have a Pioneer DV600AV DVD player. This is set to 16:9 compressed. This is supposed fit the correct 4:3, 16:9, letterbox as appropriate - it does most of the time! Sometimes, e.g. Beatles 'Yellow Submarine' and 'A Hard days Night' DVDs which are full frame 1.66:1, we have to use the zoom mode otherwise it's black bars all around the image!