Well, you could start with 1.401-1(a)(2), which requires a plan to be a definite written program. Beyond that, I'm not certain that the Code or Regs say, in precise wording, that the plan must be operated according to its terms. (They might, and I'm just not aware of the specific reference)
However, it is SO well established that a plan must be operated according to its terms, and to not do so is a disqualifying event, that it would be absurd to argue otherwise. You could refer your client to, among other things, Revenue Procedure 2013-12, which defines operational errors as disqualifying events.
Although you can correct operational errors under 2013-12, one of the requirements for self-correction, which IRS auditors look for, is some documentation of how such errors will be prevented in the future. So it isn't a never-ending pass to ignore the rules.
I think most TPA's struggle with similar clients. I'm continually astonished at how many clients hire us to do plan administration, then ignore what we tell them to do.