I don't think it's a "well known fact", I think it's propaganda. Where I worked, there was no separate pay scale for men and women. Every one in the same job and the same length of service was paid the same. Now let's look at the Postal Service, police and fire fighters, etc. Same pay regardless of male or female. I don't think any employer could get away with paying men more than females for the same job. If you can provide a real world example, I would like to see it.
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I'm thinking that if you are running from the law, you wouldn't be staying around people you know, I'm thinking you would move to another state and take on a new identity. That's where the living as a woman comes in.