Unfortunately, the repairman is probably correct. If the rear tub bearing goes bad on these washers, or if one of the spin basket drum supports breaks, it usually requires the replacement of the internal spin basket. One simple test you can do yourself is to open the washer door and place your hand inside the drum at the 12 o'clock (top) position. Push straight up and release. If there is any play in the drum, this usually means one of the rear spin basket supports has broken, or the rear bearing is bad. Unfortunately, the only way to make this determination is to take the washer part and remove the outer drum shells. If the spin basket supports are intact, the drum bearing is molded into the rear drum shell. The bearing usually is not removable, which requires the replacement of the entire back shell. This is a maintenance intensive repair that usually takes a trained technician about 2 hours to complete. Even if you attempt the repair on your own, the spin basket alone costs over $300. The rear tub shell (with the bearing) is about $345. You may try contacting the manufacturer to see if there is a warranty on the spn basket. You can use the following link to see what warranty informaiton may be available on your appliance:
It has been my experience that overloading the washer can contribute to the premature failure of the bearing and drum supports, however, there have been some cases where the spin basket supports prematurely failed due to poor welds or corrosion. These washers are usually very reliable and should last many years with proper care.
I do not necessarily agree with the repairman's assessment on the drain pump, however. If the drum slipped off the support mount springs while running, the washer would not have completed the cycle and would have shut down. This would have left any water that was already in the tub unable to be drained. If the tech performed a diagnostic test AFTER the drum was put back in place and the water still would not drain, there should have been an error code present on the front panel display of either "F02, F21, or "SUD".
If you have any questions, please post back and let me know.