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NTSB will leverage the investigation to recommend that Tesla put more safeguards in place. The NTSB - as well as all established car manufacturers - are of the opinion that every step along the way to automation should be strictly safer. That is, they believe that introducing new types of accidents is bad, even if more common types of accidents are prevented. They'll try to force Tesla to follow this status-quo thinking.
Tesla believes in a statistical approach. If Autopilot results in fewer accidents, then its a win. Sure, the car will happily drive straight into a concrete barrier if the driver isn't paying attention, but it will avoid so many other types of accidents that it is a worthwhile tradeoff. Unfortunately for Tesla, even though the general public in theory understands and agrees with the statistical argument, all it takes is one X driving into a concrete median and they'll forget all about it.
It's not so much a matter of trust. Both parties have good intentions. It's a question of which approach you prefer to get to the end-state (which is - ideally - no accidents). The first approach means that accident types and rates are strictly getting better. But progress is very, very slow. This is the Cover-Your-Ass approach that most automakers take. You don't get sued when things are strictly better, even if they don't get much better, and it takes a long time.
The second approach means that strange, new accidents can and do occur, but progress is much faster. Tesla believes that this approach will get the whole world to a much safer and automated future state much more quickly than the first approach. They're probably correct. But then they're exposed to lawsuits.
Not that this is the reality we live in but consider motivations from a different perspective:
NTSB exists because of accidents and Tesla makes money on Autopilot sales (after recouping investment in hardware). Therefore, in a dark and twisted world, Tesla has a greater motivation to get the system right but they also have a greater motivation to pass the buck while the NTSB has a greater motivation not to solve all accidents regardless of software, hardware, or wetware solutions.
In the meantime, knowing some NTSB investigators (but not leadership) and experiencing Tesla's efforts (despite communication issues), I'm incline to trust both to the extent possible knowing the truth is somewhere in between.