That's right - not a "Backup Plan", which most DBA's already have, but a "Recovery Plan". What that means is that you are working towards the end-goal - a recovered system.
Your Recovery Plan will certainly contain your backup plan, since you can't restore a database that isn't backed up. But the Recovery Plan has more - it contains the steps you need to take to repair or recover a database, including what to do with a database that goes offline and the locations of the backups, and the dates and times you've tested the plan. You simply cannot wait until you've had a failure on your system to see if you can recover it. That will not cover any Service Level Agreements (SLA's) you have in place with the business.
Imagine if you called a car mechanic to see if they could do some work on your car. They tell you "sure - we have all the parts you need and mechanics that are ready to go." Imagine now you take your car in, and it takes a ridiculous amount of time to fix the car. When you inquire about the delay, you're told, "Well, we've never actually done this before. We have everything ready in case your car failed, but we haven't ever tried to work on a failed car." Wouldn't you ask why they would advertise themselves as mechanics when they've never even practiced their craft? Well, the business has the same thoughts about IT.
The point is, it isn't enough to come up with a Disaster Recovery plan (which includes the Recovery Plan, by the way), with all of it's emphasis on the RPO (Recovery Point Objectives – The data you could afford to lose if a disaster occurs) and RTO (Recovery Time Objective – how long it will take to bring the system online after a disaster). You need to ensure that you actually can recover the system. And the only way to do that is to practice. I know this can get expensive, especially if you have a huge database. But you have to convince the business that it's worth it to set up a recovery system to practice on. If they balk, use the car analogy. Imagine a car shop that refused to allow the mechanics to actually repair a car before the shop opened.