They can say anything they want to. However, if he is letting you work right now, but continuing to accuse you of stealing time, etc. that's an indicator they may just end up warning you.
But suppose they keep arguing with you about this. And then one day they call you in and fire you. That will certainly help your chances of being approved for unemployment benefits, which you would file for immediately after you are fired. DO NOT QUIT because they are accusing you. DO NOT sign a letter saying you resigned to "protect your reference" or anything like this.
Tell them calmly and professionally that you cannot prove anything, that they will either have to believe you or not, but that is all you can do. Keep showing up for work until they tell you not to come back, that you are fired. Legal for them to do it if they want to, but if they cannot prove that they had a valid misconduct reason to fire you, you will be more likely to get approved for benefits. If they are accusing you of total terrible awful gross misconduct, the "theft of time" they are referring to, they should have fired you immediately as soon as they found out for sure you had been asleep in your car. That they're letting you linger and supposedly gather "proof" of where you have been and if you have stolen time before, they're just threatening.

