Yes. If it says "cleric X" then the oracle can use it as a spell of level X. The only reason some spells say "cleric X" instead of "cleric/oracle X" is because the oracle wasn't around until the APG.
To be even more clear, the Cleric/Oracle spell list is one spell list for both classes in the exact same manner that the Sorcerer/Wizard spell list is one spell list for both of those two classes.