You've probably all been there at one time or another. You're riding along on a multilane surface street (two or three lanes moving in each direction), and because traffic is heavy you're nosing along in the far right lane, which is relatively uncongested because it's midday and not rush-hour, and because the occasional car is parked there.
So you're feelin' good, passing all these cagers on the right, making good time, moving along briskly and ... holy crap! A car or truck suddenly shoots across your field of vision left-to-right through a gap in traffic. Some fellow drivers moving in your direction, trying to be good Samaritans, stopped and left a gap for the oncoming vehicle to pass through. Problem is, you were heading right for the conflagration, and because other cars were between you and the oncoming gap-shooter, you didn't see the offending line-cutter till it was too late.
If you stopped your bike in time, you were lucky. You were obviously riding in control and were ready for such antics. But a lot of riders in that same situation get walloped, and badly. An industry colleague we know got whacked in such a scenario, breaking four ribs, puncturing his lung and compound-fracturing his right arm. It's been six months and he's still not even close to being back to normal. And since he's in his 40s, he may never be the same.
So do the right thing. If you're gonna practice the right-lane crawl, do it slowly, sit up straight and high in the saddle and focus your attention on the lane(s) to your immediate left, the ones moving in your direction. Try to see above them if you can; doing so may allow you to see an oncoming car that's stopped and trying to nose into a gap left by folks trying to "be nice."