So, I've heard this before, and used to be in the same boat. It's not true anymore - you can gear up to decent raid levels without going to raids now, especially with the recent instance additions. It'll take longer than if you were raiding the whole time, but it's not that difficult. You do have to run Heroic 5 man instances though - no way around that.
With the changes they have made to the instances though they are much, much easier to run these days than they used to be in BC. Do the daily heroic each day (30-50 minutes) and you will quickly get enough badges and rewards to be running in one of the entry level raids, keep it up and you can get well beyond the 3000 DPS you mentioned. It takes some patience if you don't have hours to devote to running instances, but one instance each day you can log in should be your first priority if gearing up is what you want to do.