It depends on how the SPI CLK output of the SPI master is configured by the firmware:
If it is configured as open drain output a pull-up resistor is needed.
If it is configured as push-pull output no pull-up resistor is needed.
I don't know the PIC Microcontrollers but I assume its outputs can be configured as open drain output. In that case a pull-up resistor is needed.
It'd be better, however, to configure it as push-pull output, because that results in shorter rise times for the CLK signal and saves power while the signal is in Low state.
Normally it should be possible to configure it as push-pull, because there is only one master that drives the SPI CLK signal (Open drain is only needed if there are more than one (possible) devices that drive the same signal line; the resulting signal then is a "wired-AND" of all output signals connected to the line).
So you are right: it shouldn't be necessary to have a pull-up resistor at the SPI CLK line, provided the output is configured as push-pull.