It is thoroughly inappropriate to respond to legitimate criticism, made in good faith, published in a reputable journal, with a lawsuit.
It doesn't matter if you're right. If you're right; arguments can be made to show that your opponents are wrong (and he was in fact allowed a rebuttal letter in PNAS). Filing a lawsuit breaks any semblance of civility of discourse and dispassionate pursuit of truth; and results in everyone worse off, as the discussion has become thoroughly toxic.
It's burning down the entire house because someone disagreed with your analysis.
Whether it was appropriate or not depends on whether the criticism was legitimate or not. That is the legitimate purpose of legal proceedings to determine.
It doesn't matter if you're right. If you're right; arguments can be made to show that your opponents are wrong (and he was in fact allowed a rebuttal letter in PNAS). Filing a lawsuit breaks any semblance of civility of discourse and dispassionate pursuit of truth; and results in everyone worse off, as the discussion has become thoroughly toxic.
It's burning down the entire house because someone disagreed with your analysis.