The gemara brings a proof from a baraisa that the case of our mishna must be when they are not joined, otherwise what chidush is there in specifying a dry hand over a wet hand (if that hand directly touches the kodesh, whether wet or dry it will make it tamei).
But there is a difference if its dry or wet, because if its wet it makes the kodesh a sheni and if its dry it makes it a shelishi?
Artscroll note 23 say that the issue is here is only the gezeira that the kodesh becomes a shelishi, in which there is no chidush of wet or dry.
But maybe its only teaching that by a dry hand it'll make it a shelishi and by a wet hand the rabbanan increase the gezeira to a sheni!
Tzvi, UK
The Gemara is looking for a chidush in the fact that it is a dry hand. In other words the Gemara is trying to find a chumra of a dry hand. The chumra that the Gemara finds is that even though they are not joined it is still metamei derabanan. If we would say that the difference between a wet and a dry hand is that the dry only makes the kodesh a shlishi this would be a kula of a dry hand; that a dry hand is more lenient than a wet one, but we are looking for the opposite.
Best wishes
Dovid Bloom
Follow-up reply:
We learn from Rashi DH Ee Amrat that the chidush of the dry hand is that even though it is dry; and one should have thought that it would not be metamei; even so it is metamei.
Rashi writes that the rebuta of the dry hand is that even though one need not be concerned that the dry hand has touched liquids, even so it is metamei because of a Ma'alah deRabanan that the first hand is metamei the second hand to make it sheni like itself.
KOL TUV
Dovid Bloom