When one creates a US seller's account on ebay, one is required to
give credit card info- name, billing address etc. in addition to a
checking account and routing number. Obviously, the credit card is
checked right away to confirm that the name and address matches the
credit card number. However, does ebay have a means of verifying and
matching the checking account number with the name or does this simply
go on file? If it is checked, is it done automatically as with the
credit card or manually at a later date? My suspicion is that yes, it
is checked and verified, but then that would mean that the bank would
just turn over account details to ebay which doesn't seem quite right.
I would like to know for sure.

I suspect that eBay will not tell you for sure (and only they could) -
because any information of that kind could be abused by credit card
fraudsters.

You are probably correct, but perhaps there is an ex employee out
there who can clarify things or someone familiar with the banking
system. I am uneasy about ebay having all of my info. Did you know
that if they receive a request on letterhead of any law enforcement
authority for all your personal info, they will happily hand it over?
Even for people like myself who do nothing illegal, this system can be
used by the fraudsters to learn far too much about you. Ebay is more
concerned with appeasing law enforcement and avoiding major lawsuits
in the process, than they are about protecting your privacy.