Levandowski is asserting his right to remain silent and right now that is sinking Ubers ability to fight any preliminary injunction, given he is working in the exact leading capacity at Uber that these files pertain.
Though it is difficult to imagine what he is going to say to counteract the very strong impression of some cloak and dagger data theft. And even if against all odds he comes up with some believable story, it's not like Waymo need him to make their case. IIRC, the start of this whole case was some board manufacturing house sending Waymo an Uber design that looked very much like their own. So the moment they move into expert testimony on the similarity of the two product designs Uber is going to be royally screwed.
So yes, he can be fired for this. What that would achieve, other than looking like an admission of guilt (ironically this may guarantee his continued employment at Uber unless they are prepared to give up their self-driving car department entirely to this case. He may be very sure about his position until this case - and all the appeals that follow are entirely done. After that, yeah he'll be fired. That's a decade from now).
Frankly I do believe that the odds are good that Mr. Levandowski has in fact hired a lawyer, and has decided that the would rather use the protections the criminal justice system offers him personally rather than risking $600 million (or more) and jail time.
The problem is that anything used in a court case becomes part of the public record and can be used in other court cases, including the separate criminal case against Mr. Levandowski.
So may I ask, if your lawyer told you that. You own, let's say $700 million. You could either maximally defend your employer, and through that risk 85%-90% of your net worth and jail time, or you could maximally defend yourself and create as high a burden as possible for Google/Waymo to achieve anything against you personally.
If his contract either with Uber or Google conflicts with this, I believe (without research) that it does not matter : a contract does not have the necessary weight to override constitutional amendments unless explicitly permitted in the relevant amendment. Google has filed a police complaint, thereby offering this option to Mr. Levandowski, and there's no backing out now.
I believe any good lawyer would tell Mr. Levandowski to do this. For very, very good reasons.
But that doesn't mean that his legal strategy jibes well with Uber's strategy. Uber and Levandowski are joined at this hip in this case, but they have different fears and motivations. I just wonder if Uber would have a better chance if they parted ways with Levandowski and turned this into a three-way conflict. There have clearly been some differences in legal strategy between Levandowski and Uber.
His primary concern should be his own future and well being. At the same time, from Uber's perspective, if a key employee is refusing to help your defense by withholding information (something he is legally allowed to do), then the only leverage you have over them may be their position in the company.