It may sound unnatural to you, but when people panic and fear starts to set it, it may be very convincing. The fact they can even try to replicate your voice off a few words is enough for me to continue letting calls go to voicemail unless it's a saved contact. I never all unknown numbers back. If it's urgent, they'll leave a voicemail with my generic voicemail greeting.
My mom and dad were both scammed. Luckily we were able to get back the funds on one, but the funds were lost on the other. I spoke with my mom and basically came up with system for her to verify if any future "emergency" so it doesn't happen again.
It's so sad the effort people go through to scam others. They need to take all that time and effort and do something productive.