I don't buy it. Introverts do like being alone, because it's how they recharge. They can still get lonely, though, and can still be very outgoing and enjoy people.
The most difficult thing must be to be an extrovert who is shy or has social anxiety. Extroverts like having people around, and being alone drains them. But that doesn't mean an extrovert is automatically outgoing or that they really enjoy people.
OP, you sound like an extrovert with social anxiety.