Bavli, Shabas 51 amud 1, in my own loose translation:
R. Nachman said to his servant Daru: "Insulate some cold water for me, and bring me water that a non-Jewish cook has heated."
R. Ami heard and got upset.
R. Yosef asked why he had gotten upset. [After all, R. Nachman] had acted in accordance with his teachers: one [statement] like Rav and one like Sh'muel. Like Sh'muel, as R. Y'huda said Sh'muel had said one may insulate cold water; and like Rav, as R. Sh'muel b. R. Yitzchak said Rav had said anything eaten as-is, raw, has no issue of gentile's-cooking.
[The answer is: R. Ami] holds an important person is different.
Rashi explains the last line:
An important person is different: for someone who sees him being lenient will proceed to be even more lenient.
To what leniencies or types of leniencies does this latter concern apply? Just as one example, one is allowed to set up a site outside his city on Shabas to serve as his "base" for Shabas (eruv t'chumin). Would R. Ami say an important person cannot? But that's just an example: I seek to know what R. Ami's statement's parameters are in general.