As far as I can tell, the Texture specified in the Texture Panel is not
used with the Clone tool at all (Texture Mask is still effective
though).

(it is a bit of a different story in the Image Editor, the Clone tool
works a little differently there since you have to choose a clone image
in that case).

For 3D view projection painting, I would suggest the following for the
Clone tool:

• remove the Texture from viewport stencil drawing
• remove/deactivate the Texture panel

Taking a step back, one could even argue that this is true for other
tools as well (Smear, Soften, Mask, I am looking at you), so I am not
sure if this is more of a Design decision or how to handle these...