<<<One more thing she said is that I can expand my services by signing the HUD.>>>
So, are you going to get your fee as a signing agent, AND another fee for closing agent? If not, then no siggy.
<<<The Manager said that she has always asked the Signing Agent to sign the HUD >>>
She can ask me anything she wants, it doesn't mean I'm going to oblige her. 
I have never signed the HUD as "closing agent". They are asking you to swear that YOU prepared the documents, which we all know, you didn't.
Like the others said, she's blowing smoke. My .02
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