The inference is false in both directions. Although String is a subtype of Object, generic type invariance means that neither Vector<String> nor Vector<Object> is a subtype of the other. If a string vector could be used as an object vector, an arbitrary object could be inserted into storage promised to contain strings. Conversely, an object vector may already contain an Integer, so it cannot satisfy the contract of a string vector.
Both parameterizations are subtypes of the ordinary class Object, but this does not create a subtype relation between their element parameterizations. For a view accepting vectors with different element types, Vector<?> is appropriate; a Vector<? extends Object> similarly allows retrieval as Object without arbitrary non-null insertion. A Vector<? super String> accepts insertion of strings but does not promise that retrieved elements are strings. The stated subclass relationship does not hold: mutable generic vectors are invariant.