As far as I can tell, UMD does not work that way.
This skill does not let you actually use the class feature of another class. It just lets you activate items as if you had that class feature.
Unlike with other sorts of magic items, the wielder can use
What? No, UMD does exactly what the OP wants. From the SRD:
This use of the skill also applies to other spell trigger magic items, such as staffs.
Since staffs always use your CL if it's higher than their base CL, a Red Wizard can absolutely UMD a
staff of holy word and use their boosted CL.