Most of the scholars seems to indicate that the lack of information in a hadith is a proof of something being allowed. For instance, it is ijma' on the fact that taking a bath on friday (or to the friday prayer) is not fard. This is due to some ahadith and other facts which seems to mention wudu as something accepted. In the same time there are hadiths like this:
While Umar (bin Al-Khattab) was delivering the Khutba on a Friday, a man entered (the mosque). Umar asked him, "What has detained you from the prayer?" The man said, "It was only that when I heard the Adhan I performed ablution (for the prayer)." On that `Umar said, "Did you not hear the Prophet saying: 'Anyone of you going out for the Jumua prayer should take a bath'?".
While it appears in this hadith that one should take a bath when coming to friday prayer, scholars argue that because it is not mentioned in the hadith that the man (or Uthman) went home and made ghusl, or that umar didn't command him to make it, that it cannot be wajib, because of its importance, it had to be mentioned in the hadith then!
The maliki scholars also argue that because it isn't mentioned in this hadith, that the man had to wash his shoe seven times after he watered the dog with it, the dog cannot be impure (najis), rather it is pure (tahir). While the other scholars would argue that because it isn't mentioned in the hadith that he didn't wash it seven times, doesn't prove that he really didn't or that it is tahir.
The hadith about the woman who the Prophet married away to a man. Her wali (guardian) is not mentioned in the hadith. The hanafis might say "because it isn't mentioned that she had a wali, it is not needed". While the other schools might say "the lack of information about her wali in this hadith doesn't prove there was no wali there".
In the cases I just provided we have different conclusions:
- lack of information in the hadith is not a proof
- lack of information in the hadith is a proof
Now, these rules or conclusions seems to be subjective to ones already drawn conclusion, and same scholars seems to use both rules in different texts.
Is the lack of information in a hadith a proof of something being allowed?
For instance, in case 1, in the hadith, contra arguments could be given like that Utman already made ghusl before, but broke is wudu in some way and had to do wudu again. I think Ibn Hazm (of the Dhahir school) hold the opinion that ghusl in fridays were fard, so he might have had this contra argument if i remember right.