If a mathematical technique helps understand and predict nature, why not use it? The quote criticizing the method misunderstands it. It's certainly not "wrong" or "absurd."

I dislike the paper because it is sensationalist and highly misleading. For example, as far as I can tell, Karplus and Kroll didn't "confess" to anything (no direct quote is provided in the paper); we just have a secondhand assertion by Feynman. Nothing they did is "fraud," as the author claims - this is false and defamatory. Further, the issue got wrapped up by Petermann in 1957; the author is just annoyed that he didn't publish full details of the calculations. The suggestion that there is somehow lingering uncertainty is just wrong.

I no particular wishes for the author, other than that he cease writing bad papers.