Even 50,000 years ago there would be less than 1% DNA trace. This author is just ignorant. My Great Great Grandmother only gives me 12.5% of her genes so my 4th great grandparents would give me about 3%. That is a long way form 50-80 thousand years ago.
Making, of course, the huge assumption that you only have one neanderthal ancestor, and assuming that none of your ancestors married cousins.
Any particular one, yes....but summed over the entire tree?
Suppose the general population was 99% Homo sapiens sapiens, and 1% Homo sapiens neanderthalis. Now with complete intermingling, 5 generations later you have 32% of the population having that 4% (actually 3.125%) neanderthalis, with the remaining 68% being pureblood sapiens.
Now either the intermingling stopped (leaving the split at 68-32), or continued, making roughly everyone at 1% neanderthalis.
Of course other possibilities exist. Some of the neanderthalis may have died out without reproducing, etc.