I have no reason to doubt Lindsey's integrity. In addition, I did respect him for having the courage not to lowball the cost of the Iraq war.
Regarding Bartlett, Bartlett is expressing Anderson's sentiments in that quote you cite. Martin Anderson goes a bit further, he names the guilty parties who plagued the Reagan economists with exaggerated and false claims about their program (Jude Wanniski and George Gilder, just to spoil the suspense).
I agree that those "guilty parties" did hurt the Reagan cause. In addition, I think that their magical thinking is dangerous to the financial health of our country. Accepting that cuts in income tax rates have benefits and costs allows there to be a needed rational debate about whether those benefits are worth the costs and whether those costs are affordable. Believing those costs to be a "free lunch", however, makes that debate appear to be unnecessary. It would be as dangerous as a belief that government spending has such magical stimulative effects on the economy that the spending pays for itself.
That's been my worry as well, and I wonder if we aren't seeing that scenario played out right now. Politicians are no more likely to want to read economic studies and memoirs than anyone else, and they are just as likely to subscribe to the Everybody Knows school of financial history. When that history has been distorted by over-enthusiastic and less than scrupulous cheerleaders you have the recipe for big trouble.