It would help to note concrete examples when the logic fails to work, so that a future person trying to fix this knows what concrete issues to tackle.

I'm going to prepare design doc for refactoring. That should probably include than refactoring only this function.

I'm stumbling on failures of PasswordFormManager::DoesManage
Does the doc exist yet? It would be nice to be able to check my case against a list of known failures.

No there is no yet design doc. This refactor will be part of a bigger refactoring. The bigger refactoring is postponed to Q4. I can answer you questions about this code offline, I'm pretty familiar with it.

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PasswordFormManager will be replaced soon (bug 831123). So this bug is obsolete.