Checking if the lift drums need resetting: The old position of the lift drums on the shaft may have slipped or otherwise lost the the proper position, requiring a reset of the drum position on the torsion shaft. You will also reset the drums if you are replacing the lift cables, since the new cables will not exactly match the length of the old ones. Problems like uneven tension on the cables, or a tilted door, or a door that doesn't easily stay aligned with the tracks, can be due to an improper "set" of the drums on the shaft. So one shouldn't assume the old positions are correct. Setting the drums on a "fresh" part of the shaft will avoid the possibility of damaging the shaft from retightening in the same dimples.
The "safety issue" trick: Another tip-off is the use of language like "safety issue". This is meant to trump any objections you might have to a costly repair bill. Don't be manipulated by the suggestion that you are risking disaster if you don't buy something expensive. Even if you think the risk is genuine, get another estimate, and tell the second repairman you are skeptical; every technician loves to prove the competition made a mistake.
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Resetting the drums, if needed: If the drums were incorrectly set in their old positions, one must reset both drums in new positions on the shaft. This is complicated by the presence of old dimples in the torsion shaft from previous setting(s), which must be avoided lest they improperly influence the new setting of the drums. To begin this process of resetting the drums, the door must first be lowered and resting level on the floor, the spring(s) must be in the unwound condition with their set-screws loosened, and the lift cables wrapped around the drums. If for some reason the door does not rest level on the floor, such as the floor being uneven, then insert temporary shims between the door bottom and the floor to bring the door up to level. Loosen the set-screws on the drums, and turn the torsion shaft to avoid the old dimples from the set-screws in the old drum position. Tighten the set-screw on the left drum (that is, on your left as you face the door from in the garage), creating a new dimple, and apply tension to its cable with the locking-pliers technique, enough tension to keep the cable taut but not enough to start to move the door up. Attach and wind the cable on the opposite (right) drum by hand until the cable is similarly taut, and set the screw, remembering that tightening the screw will tend to add a bit of extra tension to the cable. Both drums should now be fixed on the torsion shaft, with the cables about equally taut (listen to the sound when you pluck them like a guitar string) and the door still level on the ground. Setting the left drum first, and the right drum second, will allow you to take up any slack in the cable introduced by the left drum rotating slightly with respect to the torsion shaft as you tighten the set screws. This alignment and balance of the cables, drums, and door is critical to smooth operation and proper closing. If you have a single-spring assembly, the distance along the torsion tube from the spring cone to one drum is longer than to the other drum, which allows a bit more twist to one side than the other, and you may have to compensate with the setting of the drums. 

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