Changing the texture of materials

Am I correct that once you make any item a component, paint it with any material, you can no longer change the texture. Context clicking on the material does not give you the option of selecting “texture”.
See SU texture test.skp (53.7 KB)
The 2 rectangular items were made components. The circular one was not.

No !
You CAN change the textured-material of any component-instance or group, by repainting it with another material.
If you have applied a material onto a face inside a ‘container’ [component/group], then you can edit the container and apply any other material onto any chosen face…
BUT if you want to change a material’s texture [globally], then use the Material Browser’s Edit tools:

No, you are just looking for it in the wrong place. There are several ways to go about this. As TIG said, the easiest is probably to just paint the entity again with a different material. Another is to open the Entity Info window and click on the little material sample shown there. That should open the Materials window and let you select any other material to replace the current one.

Thank you both. I finally got back to this and followed the suggestion and of course that did the trick.