The definition of a secondary battery is "rechargeable". Primary batteries, by definition, are not capable of being recharged easily or effectively. So saying "primaries are not rechargeable" and "secondaries are rechargeable" is redundant.
Also, there are Li metal anode secondaries. And you are apparently thinking of the cathode when claiming that the Li metal anode is replaced by a lithium oxide material. Typically, the Li metal anode is replaced by a graphitic carbon anode, into which Li ions intercalate.
jvn