Yep, the copper washer squashes up and forms a good seal on the drain plug. Reusing the old one may not seal properly since it has already been squashed. It really isn't worth risking an oil leak for £1 (or probably $1 for you!)
Here's a picture of my old drain plug with squashed washer and my new magnetic one with a new washer on:
I changed my oil for the first time yesterday. Thanks for this guide. The suggestion of using the electric driver on the bolts and the water bottle as a funnel was inspired and saved me loads of time
