If you're driving and you're too tired, it wouldn't be hard for a police officer to assume that you were under the influence of alcohol. After all, a lot of the signs that police are looking for show up when you're tired, as well.
Part of the problem is with field sobriety checks. You may stumble while walking on a line because you're exhausted, but the officer doesn't know if you're tired or drunk. You may not be able to recite the alphabet perfectly for the same reason.
In fact, this has happened. One man was stopped at a checkpoint and officers thought he was drunk. He said that he wasn't, and ended up getting arrested when he wouldn't do the sobriety tests. The officer told him he had to do the tests, which was false, and decided to arrest him. He was then taken to jail and forced to have his blood drawn so they could test him that way.
The man was not drunk. He was not on drugs. The blood test that he was forced to submit to proved it.
There is a twist ending to the story. Though the man was arrested, he later sued the police department for arresting him when he had not broken any laws. He won the case, and he got $70,000 for his troubles.
As you can see, it's very important to know your rights whenever you are accused of driving under the influence in California, and you also need to know what legal options you have if you're arrested when you're sleepy, not drunk.
Source: Counter Current News, "Sober Man Arrested At Checkpoint For Being Sleepy Awarded $70,000," Jackson Marciana, accessed May 12, 2016