I seem to recall that one of the reasons for saying the more specific Bracha before the less specific Bracha is that since Bdieved one is Yotze with the less specific Bracha, once he says the less specific Bracha, he is no longer obligated (or allowed) to make the more specific Bracha. However, I don't recall the source. If it so, then even in a case of Haetz and Adama, one should make the Haetz first.
RASHI (41a, DH Aval b'sh'Ein) emphasizes that one cannot fulfill his obligation to say a blessing on a specific food by saying a less specific blessing on a different food that b'Di'eved works for the first food. That is, even though if one recited "Borei Pri ha'Adamah" on a fruit he is Yotzei b'Di'eved, nevertheless if one recites "ha'Adamah" on a radish, it does not cover the olive that he also has in front of him.
This is also the reasoning of the Rishonim who maintain that there is no precedence of "ha'Etz" over "ha'Admah." Consequently, the only reason why some hold that "ha'Etz" does come before "ha'Adamah" is not because "ha'Adamah" could exempt the fruit from its blessing, but because the blessing of "ha'Etz" itself is more important due to its higher level of specificity.