Data Matching Using Machine Learning
You can obtain one negative example by taking one of the 3000 customer records and pairing it with any user record that is known not to match.  In this way, you can obtain $3000$ positives and $3000 \times 5999$ negatives.  You could then train a boolean classifier on this entire training set.  This might work better than using one-class classification on just the positives.

Even better might be to use techniques for learning to rank.  If $c$ is a customer record that is known to match a user record $u$, and $u'$ is any other user record (which $c$ doesn't match), then you want your classifier to rank the pair $(c,u)$ higher than $(c,u')$.  In this way you can obtain $3000 \times 5999$ such ranking-pairs, and try to train a classifier to learn to rank, then use that to find the best match for each of the 1000 customer records.