Although I don't see how Clement's bulls in support of exposition can be apolitical while his caveat can be dismissed as 'political' . . . my impression of Clement VII is that he was WHOLLY political! He was in a precarious position in Avignon. The convolution of the church with the nobility and the infighting amongst the various factions of the nobility certainly makes for interesting reading . . . but it also most certainly obscures the truth.
I think you misread shroudie on this point. The caveat that the Shroud may be exhibited with the announcement that it is a "representation" IS entirely political BECAUSE of the dispute between Lirey and the Bishop. The Pope found a way to mollify those putting pressure on the Bishop as he SILENCED the Bishop on this subject, and still allow the exhibition of the Shroud which the King of France had already approved. Everybody walked away with something. Political... and good politics at that.