We present Very Large Array (VLA) H i imaging of four low surface brightness (LSB) galaxies ([OBC97] P01-3, [OBC97] C06-1, [OBC97] C04-1, [OBC97] C04-2), 1 which were thought to strongly deviate from the Tully-Fisher (TF) relation based on Arecibo single-dish observations. We do not detect three of the four targeted low surface brightness galaxies (LSBs) in H i down to a 4 limit of 0.08 Jy km s À1 . We find that two of the four of these LSBs have bright galaxies at projected distances of 2<6 and 2<9, which have contaminated the Arecibo signal. A further examination of the Arecibo sample shows that five out of the six galaxies that were found to deviate from the TF relation have nearby bright galaxies (within 3<5 and within the observed H i velocity range), and we conclude that possibly all but one of the non-TF galaxies are contaminated by H i from nearby galaxies. The sixth galaxy was not detected by us. A new observation by Arecibo did not confirm the earlier detection. We present the H i properties, kinematics, and rotation curves of three bright galaxies NGC 7631, KUG 2318+078, NGC 2595 which happened to be in the LSB fields and of two LSB galaxies, one of the targeted ones C04-2 and one (UGC 12535 or P01-1) that was found in the field of P01-3. The two detected LSB galaxies fall within 2 on the TF relation. The integrated profiles of the bright galaxies are consistent with the Arecibo results both in velocity range and amplitude, which indicates that most of the extreme deviators from the TF relation must have been affected by bright companions in this earlier H i survey. A more recent determination of the sidelobe structure of the Arecibo beam supports our conclusion and shows that the degree of sidelobe contamination was much larger than could have been initially predicted. If the now unknown velocities of these nondetected LSB's are within our probed velocity range then the limit to their H i mass is roughly 10 8 M assuming H 0 = 75 km s À1 Mpc À1 . Hence, we have corrected the results found in O'Neil et al. (2000a) and have reconstructed the TF relation. These new observations then show (1) a reconstructed TF relation that has relatively large scatter at all values of rotational velocity (possibly indicating the true range in disk galaxy properties) and (2) the presence of at least some red, gas-poor, LSB disks that indeed may be in an advanced evolutionary state as the faded remnants of their former high surface brightness actively star-forming state.