I guess my question is:
Are you just asking whether there's a problem with a person using the same online user ID to access both his business and personal account, or are you saying the accounts would be tied together on online banking and that in addition to simply accessing the data, the person could conduct cross-account transactions?
One thought that comes to mind even in the pure information-only context is that you would only want to assign a user name and password to an individual who is the duly appointed authorized signer for the business entity -- not every stockholder, for example. (Imagine every shareholder of AOL getting a peek at the checkbook, for instance.) Authorized signers typically change over time. If you have assigned the same user name and password to an individual as you have to a business he's affiliated with, you need to figure out how you will be able to cut off access/change the password, whatever, when the individual is no longer affiliated with the business or is no longer an authorized signer on its account.
And I agree with Al that if you're talking about transactional capabilities, you have a whole other can of worms.