Hi: Your trans mechanic is correct. A P1875 deals with the lo-lock 4wd. The transfer case module sends a signal to the engine computer when it goes into 4wd low so the engine will shift the transmission differently. First thing to do is to check the connector to the transfer case module, The transfer case module(TCCM) is located behind the passenger side kick panel (to the right of where the front passenger's feet go). Check the connector for water or crossion in it. If everything looks good, then chances are the module is bad or you have damaged wiring at some point.
Here is the actual meaning of the code: P1875 -- Transmission Automatic Hall Effect Sensor Power Circuit Short To Battery / 4WD Low Switch Circuit Electrical
Let me know if this helps. Regardless, the trans tech is correct.