If company A gets sued by some one planning to use the discovery process as a fishing expedition, A will fight it very hard, demand to see the court orders and will do everything possible to comply with the letter of the court order while defying it in spirit. No one thinks A will just let the discovery process go unimpeded. A will do anything short of being
convicted (not merely accused) of obstruction of justice. And it would cost money and it would take considerable risk.
If company B has a cloud provider C with iron clad contract to do everything possible to protect B's data, and B gets sued and C is dragged into the discovery process. How strong would C fight the fishing expedition? C will minimize its risk, its costs. Despite whatever the contract with B says, it is going to cooperate and will protect B's data only to the extent B will be able prove negligence on the part of C.
If some cloud provider provides only the administrative and maintenance services, but the physical servers are in your premises, with access controlled by you, discovery controlled by you, it is not a good idea to out source it to the cloud provider.
I find many software development companies outsource the entire planning, scheduling and development process to third party companies like $agiledev.com or $rapid.deployment.com or $general.scrum.com. Very very fertile ground for patent lawyers to launch archaeological expeditions, years after the fact, claiming IP violations of submarine patents.