3dTeig is setting FA values calculated on voxels containing negative eigenvalues to zero. This typically happens either on voxels with very low image intensity (like outside the brain) or very large anisotropy values (dense fibers), where one eigenvalue is very large and the other two are close to zero (with some image noise they can show up negative).
GE is setting these negative eigenvales to zero and calculating FA anyways. 3dTeig makes you aware of this situation by setting FA to zero.
Of course you can calculate FA yourself, actually 3dTeig shows the reference to that paper containing the formula during its execution.

Maybe 3dTeig should have a threshold parameter to do the FA zero setting only for negative eigenvalues more negative than a certain threshold value, which would still include these high anisotropy fibers.

Wolfgang