Wikipedia explains a false negative Rinne test

http://en.wikipedia.org/wiki/Rinne_test

Air conduction uses the apparatus of the ear (pinna, eardrum and ossicles) to amplify and direct the sound whereas bone conduction bypasses some or all of these and allows the sound to be transmitted directly to the inner ear albeit at a reduced volume, or via the bones of the skull to the opposite ear.

In a normal ear, air conduction (AC) is better than bone conduction (BC)
AC > BC, and this is called a positive Rinne.
In conductive hearing loss, bone conduction is better than air
BC > AC, a negative Rinne.
In sensorineural hearing loss, bone conduction and air conduction are both equally depreciated, maintaining the relative difference of
AC > BC, a positive Rinne.
In sensorineural hearing loss patients there may be a false negative Rinne
BC > AC, a negative Rinne.

Note that the words positive and negative are used in a somewhat confusing fashion here, other than their normal use in medical tests. Positive or negative means that a certain parameter that was evaluated was present or not. In this case, that parameter is if air conduction (AC) is better than bone conduction (BC). Thus, a "positive" result indicates the healthy state, in contrast to many other medical tests.

[edit] Hazards
This test, WITH (not and--Michelle) its complement the Weber test, are quick screening tests and are no replacement for formal audiometry.
Retrieved 26 SEPT 2008

+ Rinne  - Rinne (the criteria AC > BC not met)
AC > BC  BC > AC
normal   conductive loss
SN loss
         SN loss can be missed if pt responds here (FALSE NEGATIVE) instead of 

here       

THEREFORE, you need the Weber test to determine whether there is
SN loss. That test can detect a unilateral sensorineural hearing loss when the unaffected ear responds.

Here is the chart in wikipedia.

	Weber without lateralization	Weber Lateralizes Left (Louder in Left)	Weber Lateralizes Right (Louder in Right)
Rinne Both Ears AC>BC	Normal	Sensorineural Loss in Right	Sensorineural Loss in Left
Rinne Left BC>AC		Confirm Conductive Loss in Left
Rinne Right BC>AC			Confirm Conductive Loss in Right