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Here's how that aspect of phone switches work:
The basic idea is based on statistics that say that for any N phone lines, there will rarely be more than so many percent of them in demand. So only that many actual outgoing lines are available to the switch. If more than that many people try to call at the same time, someone gets the fast busy signal, an error message, or no dial tone.
The point is that she's probably telling the truth. Why are you having problems trusting her? That's a rhetorical question, BTW.
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