Saving a local copy of an image or off loading image load to twitter?

So in my php application I allow users to login via twitter, when doing this twitter gives me a link to their profile image. Since my site also uses profile image I was planning on taking this image and setting it to their default image until they chose to change it. So my question is there are two ways I can do it.

1) I can take the image url and save it in my DB and then every time I need to display it just link to that url which will load the image from twitter.

2) Save a local copy of the image and save that location in the database, therefore removing twitter from the process.

I am not sure which one of these is the best practice and I was hoping to do the first option however I could see how if enough people did this it could piss twitter off as they would have to pay for serving images to users not even on their site. Any info would be great