I am curious as to whether a business owner can sign a check made out to them personally.
They sure can. They are two different legal entities, so why not?
You can even write a check to yourself, and then deposit it back into your own account. (Not very useful, but you can).
The tax implications are a very different question, as this might constitute taking money out of the company.
Edit: In some countries, when the business hires someone to work for them, it is forbidden by law to do that, unless he/she is explicitly allowed to do it in his contract. The business owner himself however, can always 'allow' himself to do that.