TC, your first point is valid if there are shares
Post# of 36536
None of my purchased shares in TDA show a due bill attached; but as you yourself reported, it appears TDA doesn't show the notation. I'll watch come Monday to make sure my share count doubles, and if not, I'll be on the phone to find out why.
On your second point, I think you are incorrect. The due bill is automatically attached (see my post last weekend about the due bill system in the US); if there is no due bill attached, I can't see how a brokerage, DTC or anybody else would suddenly issue a dividend to that share. If it were a manual process, perhaps - but since it has been automated for at least 8 years, I think that your scenario of just applying dividend shares to everybody is unlikely at best, and probably impossible.