Does "even when they are unhappy about its moral probity" mean "even when they know advertising is not always behaving very morally"?
Context:
Despite (or perhaps because of) its lower status, most people feel more at home with the idea of advertising than with art, even when they are unhappy about its moral probity.
Yes. )
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Yes.
(To say that advertising is "behaving" in a certain way feels slightly odd.)