No you do not have problems with your bearings (especially if you can rotate the basket and it rotates nice and smooth).
What has happened to your machine is exactly what happened to mine: One of the three 'legs' on the shaft support attached to the rear or the basket has broken. The reason it broke is because the bracket is made of die-cast aluminum alloy that is being attacked by galvanic corrosion. See attached pictures of the corroded shaft support, including a close-up of the break. This is what you will find when your machine is taken apart.
You can verify this failure mode by slowly rotating the basket and observing the position of the basket at its maximum off-center location. While the basket is at this position look at the back of the basket and you should see one of the three 'indents' located at the 12 o'clock position. While at this position you should be able to move the basket up and down. Now rotate the basket 120 deg so that the next 'indent' is positioned at the 12 o'clock position. The basket will now be more centered in the opening, and you will not be able to move the basket up and down. You have just identified which of the three bracket arms have been broken.
Call Whirlpool warranty service (1-800-253-1301) and tell them about the problem with the basket: believe it or not the basket has a life-time warranty. The shaft support is not available as a seperate item. The basket p/n is 8182232.
I was able to get Whirlpool to send me a replacement basket, but they would not do the same for the front-half of the plastic tub, which was damaged by the basket hitting the front lip, even though the warranty states that the plastic tub is warranteed for ten years. They did however agree to sell me one for 50% off the std cost. The p/n is 285982.
If your washer was purchased less than 5 years ago, best to work with your local Whirlpool authorized service agent to get the machine repaired. My machine is over 5 years old (GHW9100LW1), and I am repairing the machine myself.
I would be interested in hearing how you make out in getting your washer repaired.
Bill in Ma.