I think the caveats are pretty clear:
Smartphone trade-in must be in good, working condition. Excludes upgrades.
How to claim this offer.
New Verizon customers as well as existing customers who want to add a new smartphone line can get $300 for their old phone.
1) Add a new smartphone with monthly device payments to your cart.
2)Complete your trade-in appraisal during checkout.
When prompted, click “trade in old device.” You will be taken to the device recycling page to appraise your old smartphone.
3) Send us your trade-in in good, working condition.
You’ll receive a box to return it within 5 days. New Verizon customers will receive a VZW electronic gift card within 2 weeks and existing Verizon customers will receive an account credit in 1-2 billing cycles.
So the 2 MAIN caveats appear to be: 1) NEW CUSTOMER (and buying new phone) OR 2) ADDING a line to an existing plan (and buying a new phone).
I don't think it matters if you're trading in an original Droid versus a newer phone as long as it's in 'good' working order. That term 'good' will probably need to be clarified better by the CSR or Sales person.