2012 Toyota Camry Hybrid steering rubbing sensation

Your car has electric assist steering (Toyota calls it EPS).
Quick, while your car is still under warranty, have the dealer to check it out for you. They've had steering sytem complaints with their EPS (so has all other car makers).
However, the main reason is because most independent shops do not have a scan tool which will recalibrate some of the parameters on the EPS. Your dealership does.

Since your car has electric power steering there are no power steering hoses.
The steering is assisted by an electric motor, whereas the older cars have a power steering pump which uses power steering fluid.
Don't forget to have the alignment checked (should be free under factory/dealer warranty).

Thanks for replying. No, you're not being annoying. This is what we're here for. Please keep your questions coming.

The bumping could be caused by improper wheel alignment. In some cases, the alignment could be out of adjustment enough to allow the wheel to be turned so sharp that the tire is scuffed along the pavement during sharp turns, which would cause some of the sensations that you describe.
Call around to the local alignment shop to see if any give FREE alignment inspections. They do this sometimes in order to "drum-up" new business. This check will let you know if your car needs an alignment.
Have the mechanic to check the intermediate shaft U-joint for looseness, if he suspects its the problem. Perhaps you can do it yourself. I'll look for a diagram.

Did the last mechanic test drive the car?
It doesn't seem normal to me, especially if it wasn't there before.
You need a second opinion. Is the service engine light on? If so have the codes read. This will give s good starting point for diagnosing the problem.

Did you have the alignment checked yet?

An alignment (also called a four wheel alignment) is a procedure which measures the various angles of all four wheels as the vehicle travels down the road and also as it turns. The process involves and alignment computer and lasers, ect. Not something that you can do without this or other specialized equipment.

The u-joint that the mechanic referred to is in the steering column where it connects to the rack and pinion steering unit (accessible underhood and underneath the vehicle). The u-joint is has a protective cover on it to keep out water and dirt. Once the mechanic or you manages to pull that cover back to reveal the u-joint, you can then, shake twist and wiggle it, checking for looseness (especially when the wheels are turned tot he right).

Another thing, start the engine and turn the wheels all the way to the left. Note how far they turn. Then turn them all the way to the right. Is there a difference? Do the wheels seem to turn sharper tot he right than to the left? (If so alignment problem.

**You still could have alignment problems even if the tires seem to turn the same amount. Most alignment problems are hard to see with the naked eye, hence the sophisticated alignment equipment.

I hope that this helps. I'm still searching for info and will let you know if I find anything that might help.