Yeah, for sure. You can dial it down. The tone I preferred was open. I think that when you roll the tone back on any bass it can sound OK, but it was not the L2K's strength. I felt it was hard to control the "clank" factor. Admittedly, I'm not the be all end all of technique or tone mind you.
I know what you are talking about. One of the things TBers have discussed a lot is that a secret of the L2000s is dialing back the tone controls just a bit. Of course I love the wide open thing too! And one way to control that is with strings that do it for you. I can say it took me a while trying various strings until I found some I liked. The factory strings were definitely not the ones.