OKLAHOMA Hourly Wage non-payment for working lunch (30 min) for 1 year.

So I'm in Oklahoma and receive an hourly wage. I work an early shift from 4am to noon most days. I'd take a lunch around 5:30 or 6am (30 min) but work through lunch because I wasn't hungry that early and didn't want to be lethargic. My employer found out and I was written up. My boss had first told me that they were legally obligated to pay me for the wages I worked. However, after she spoke with our regional HR rep, that changed. Now, since I wasn't asked or forced to work off the clock during my lunch hour, according to them, they aren't obligated to pay me any back wages. Is this accurate or since I'm hourly and not salary, they have to pay me for the time worked irregardless of the reason? Any information us greatly appreciated.