A Rights Offering for existing shareholders makes a lot more sense than looking to private equity, vulture funds, investment banks, etc... IF there's certainty the amount needed to be raised could be raised. All of those entities will want their pound or two of flesh, and probably give less favorable terms than shareholders would.
If the Rights offering was limited to 10% of a shareholders stake (as of some date of record), that would mitigate issues with selling shares to buy discounted shares... I'm not looking to tread water, so I'd be using fresh cash to increase my position... I'm sure more than a few would feel the same way.