2002 Lexus GS300 Question: O2 sensor -ck. engine light

I don't think this shop understands the basics of the P0402 code and how this emissions system works, if you did indeed have this code.
Here is some info on the P0402 code: http://repairpal.com/OBD-II-Code-P0402
This is an EGR code and the O2 sensors are not very likely to cause this code, but it is possible. What they are absolutely wrong about is that the computer will reset by driving it, not true.
Print out the info about the code, and go back to them and demand that they address problem. Or you may need to take it to a shop that understands how to work on these vehicles.