2001 Honda CRV Timing Belt broke at 100500

Took to a Honda Only shop. Told me they were going to redo the head. This took 4 days. Once back, 5 days later wife tells me check oil light icomes on and off.
I checked the oil, added 4 quarts, called the shop back. Told me to do an oil consumption test! I called them back the next day and told them an oil consumption test was already done. My wife drove it 500 miles and used 4 quarts of oil. In addition white smoke was coming out of the tail pipe.
They took it in, and sent the head back to the shop. The shop tell them its the rings not the head. They get the head back, replace it, check everything out and tell me it is ready for pickup.
They say they replaced the PCV valve, and the oil consumption dissappeared.
However, there is still white bluish smoke still coming out the tail pipe. They say it will pass emissions inspection. They say it is the rings, and the car will run fine for a long time. BUT the car did not have the smoke before the timing belt snapped.
BUT I am not schooled in cars, I only know what I read or hear about.
WHat else should they have done?
Should they have gone after the rings? The pistons?
Should I ask them what the compression test showed?
I do not have alot of funds, BUT I would like it fully repaired. Is it fully repaired? With the smoke and all still coming out? WHat am I missing here?