Imagine someone has commissioned a large building to be built - a bar, let's say - and the following conversation takes place:
Architect: For a building of this size and capacity, you will need fire exits here, here, and here.
Client: No, that's too complicated and expensive to maintain, I don't want any side doors or back doors.
Architect: Sir, fire exits are not optional, they are required as per the city's fire code.
Client: I'm not paying you to argue. Just do what I asked.
Does the architect then ask how to ethically build this building without fire exits?
In the building and engineering industry, the conversation is most likely to end like this:
Architect: This building cannot be built without fire exits. You can go to any other licensed professional and he will tell you the same thing. I'm leaving now; call me back when you are ready to cooperate.
Computer programming may not be a licensed profession, but people often seem to wonder why our profession doesn't get the same respect as a civil or mechanical engineer - well, look no further. Those professions, when handed garbage (or outright dangerous) requirements, will simply refuse. They know it is not an excuse to say, "well, I did my best, but he insisted, and I've gotta do what he says." They could lose their license for that excuse.
I don't know whether or not you or your clients are part of any publicly-traded company, but storing passwords in any recoverable form would cause you to to fail several different types of security audits. The issue is not how difficult it would be for some "hacker" who got access to your database to recover the passwords. The vast majority of security threats are internal. What you need to protect against is some disgruntled employee walking off with all the passwords and selling them to the highest bidder. Using asymmetrical encryption and storing the private key in a separate database does absolutely nothing to prevent this scenario; there's always going to be someone with access to the private database, and that's a serious security risk.
There is no ethical or responsible way to store passwords in a recoverable form. Period.