Does ISP mean that the chip has to remain stuck on the system PCB when programmed?
ISP does not require removal of chips from a PCB.


  In-System Programming (ISP) is the ability of some programmable logic devices, microcontrollers, and other embedded devices to be programmed while installed in a complete system, rather than requiring the chip to be programmed prior to installing it into the system.


From Wikipedia, my emphasis.

It is not relevant whether programming using ISP is carried out after the product has left the factory.