It is more that they used the DNA of the Neanderthal and combined with themselves such as the Annunaki
One of the problems with staple sci-fi movies is that aliens in them tend to be humanoid, looking nearly exactly humans. Mainly this is done because of the incredible expense of making a movie alien look convincingly alien. The strangest creatures that exist on Earth are at least from the same common gene pool as every other living thing on Earth. Imagine how much different an alien would be, one that came from a completely different evolutionary tree.
Take a look at the VAST diversity of life on Earth which came from a single, common gene pool. And yet, a fish can't mate with a mammal, despite what Mr. Garrison teaches above.
Now, try to imagine the DNA of an alien being, one completely outside of the Earth's gene pool. A pool which started 4 BILLION years BEFORE the Neanderthal.
How compatible would an alien DNA (assuming they have anything like DNA) be to the DNA of any creature on Earth, especially a hominid like The Neanderthal.
Now, take a look at modern human DNA, there is absolutely nothing in it that suggest our DNA is alien to that of any other animal, plant, bacteria, or virus that has ever existed on Earth.
No, I would say whatever 'evidence' exists regarding the creation of humans by meddling aliens, there is a much more prosaic, more simple, and more logical explanation closer to home.