Not true, I did exactly that the last time Amazon was having a penny sale. I did exactly what you're talking about. New smartphone to my line and an old dumb phone to the new line. The ONLY time you'll get hit with the $250 charge is if you cancel the line of service that you open with amazon before 181 days.
You can switch phones in between your lines as much as you want too. Just DONT cancel the new line of service!!
The one thing you gotta do makes it kind of a pain. You must activate the new phone on the new line of service, but after that you have to go into a store and get a new SIM card for your line unless you already have one. But regardless, just make sure of these two things:
1. Make sure to initially activate the new one on the new line.
2. Have a dumb phone on hand to replace it on the line. (I bought one off of craigslist for $10)
AmazonWireless
AmazonWireless Instant Discount Policy
When you purchase your device with service from AmazonWireless.com, we automatically pass along an instant discount from the carrier to you. This discount has been provided to you based on your agreement to (a) activate a new, or extend an existing, line of service for this device with the carrier, and (b) maintain this service in good standing for a minimum of 181 consecutive days. If you do not activate or extend a line of service in connection with this device, or if your service is canceled/disconnected before 181 consecutive days, AmazonWireless.com will charge you $250 per device, plus applicable taxes.