Saying there is a grounding flaw is putting it mildly. Having some 20 years under my belt designing and installing a pile of cellular sites over that time, I have never had a generator damaged. There have been regular lightning strikes on the towers over the years.
Sounds like there is an issue with both the "GROUNDING SYSTEM" and the "Surge Protection" installed. Not wanting to point the finger without first looking at what the engineering drawings show or what and how it was installed, I would only say it needs some outside consulting on the issue. In this case with multiple towers sustaining damage, I can only conclude that a basic flaw exists in all the towers.
Grounding a radio facility is not rocket science. The process has been refined over many years. Depending on the soil resistance, it may be easy or hard. The bottom line goal is to protect the equipment at the facility and have it survive strikes on the tower. I use the term "Grounding System" because it is more than just a ground rod in the earth. You also need to take into account telephone cables entering the facility. You need to look at the electrical power feed to the facility. You need to look at the bonding of the tower to the shelter. You need to have electrical power surge at the electrical circuit breaker panel. You need to have surge protection on all the telephone connections entering the facility. Any external items like generators and fuel tanks need to be included as part of the "Grounding System". All the antenna coax cables entering the facility need to have ground kits and surge protectors installed.
Maybe your getting the hint that no one item is all that you need. Everything at the facility needs to be connected to a common ground. This way if the facility take a hit, it all goes up and down at the same potential. You don't get any current flow between different items or devices at the facility.
Unless you have a strong background in grounding practices, the average person would not even know what they are looking at. You ask can a tower take a direct strike and stay operational with no damages. In my years of doing this, the answer is yes. I have been at a number of facilities during storms and actually seen the towers take a strike. You see the tower steaming in the rain from the heat that was generated carrying all that high current to the earth. After the storm, you go inside the facility and everything is just humming away the way it should.
Grounding a facility doesn't come easy. It takes careful planning. It takes skill on the part of the people installing all the ground rods and ground wire tying them all together. It takes skill on the part of the equipment installers to ground each piece of equipment to the rack and the rack to the master ground bar. It takes the electrical contractor to make all the grounding connections on the power surge protectors. These people and the grounding all need to work together.
There are locator devices to trace underground wires to follow where they go. It might even take digging up the ground system in several places to look at the connections to the ground rods. Spacing out the distance between the ground rods even plays a part. Generally the ground rods should be spaced out a distance equal to double their length.
OK, now that I have spilled some of the secrets of protecting a telecom facility, tell the rest of us just what you find for problems at the damaged facilities.