The answer in part seems to depend on what you mean by "human intelligence". If you mean behavior that would usually be regarded as requiring intelligence were a human to produce it, then various types machines can be intelligent.
Such "intelligent" machines presumably include player pianos. Playing the piano and producing a melody is widely regarded as requiring human intelligence when humans do it. Player pianos produce the same sort of behavior, but without a human touching a key. Hence (so the argument goes) player pianos are intelligent.
But if "intelligence" includes having the inner process of understanding, say understanding the meanings of symbols of written language, then at least according to philosopher John Searle, purely symbol manipulating devices such as digital computers could never be intelligent. This is because symbols in themselves don't contain or indicate their meanings, and all the computing machine gets and manipulates is symbols in themselves.
However, there does seem to be a sense in which the question "Is artificial intelligence really just human intelligence" is true of computers. This is when the behavior of the machine is caused by human intelligence. A human writes a program that defines, mandates, the behavior of the machine (just like a human designs the mechanism and paper roll of a player piano). This design takes human intelligence. The machine has no intrinsic, or innate, intelligence. It's just an automaton mindlessly following the causal sequence created by the intelligent human designer.
Now if computers are purely symbol-manipulating devices, and if Searle is right, AI is doomed, at lest as long as its development platform is the digital computer (and no other machine is available or seems on the horizon).
However, are computers purely symbol-manipulating devices? If not, there may be a way they can acquire meanings, or knowledge, and, for instance, learn languages. If computers can receive (including from digital sensors) and manipulate more than just symbols, they may be able to acquire the inner structures and execute the inner processes needed for human-like understanding. That is, they might be able to acquire knowledge by way of sensing the environment (as humans do). A human might write the program that facilitates acquisition of such knowledge, but what the knowledge is about would be derived from the sensed environment not from a human mind.
But here we're talking about "intelligence" defined over inner processes and structures, not or not just external behavior. If you define human intelligence as external behavior, as the Turing test does and as AI researchers often do, then music boxes with pirouetting figurines, player pianos, and programmed computers all have human-like intelligence, and artificial intelligence as it exists today is really just the same sort of thing as human intelligence.