Sorry, but those articles don't say that at all. They pertain to investigative evidence being made available to the general public (such as FOI requests). Not to defendants in a trial.
There is no legal way for the TBI to withhold ANY perhaps-relevant evidence from defendants on trial, and to do so would cause convictions in TN to be overturned right and left. Such a practice would be a fundamental violation of defendant rights as defined in the US.
The TBI are investigators, they are not officers of the court. Prosecutors have an obligation to provide discovery of all information known to them, but the investigators do not. What can't happen under law is the information only being provided to one side and not the other. Also, when specific information is requested, they have to provide it, they can't conceal it.
But, if the prosecution doesn't ask for it, and they don't provide it by tacit understanding, then that bit of information would not be available for discovery. If LE is unbiased and does a professional job, then that sort of thing will not happen - they hand over everything they have and let the prosecutor decide. But, if they are partisan and see themselves as a proactive tool to obtain convictions without regard for justice (in other words, corrupt) then these sorts of things can and do happen. On small scales it might be in the form of an individual officer "forgetting" or "losing" information and/or evidence that is inconvenient to their theory. On more institutionalised scales the practice could be endemic in an agency and their practice the point that it becomes just the way they do business.