It's usually amusing to see what happens when people start running up against the more non-sensical aspects of FLSA enforcement, but this is a sad story. It's sloppily reported by the Chicago Tribune, especially given the headline, but reflects something that employers with hourly employees must be aware of: there is no such thing as volunteer work for a non-exempt (hourly) employee. If you are working for the benefit of your employer, you have to be paid for it, even if the work is being done voluntarily during a non-paid break period.
The trouble in this particular case, in which a woman was fired for trying to catch up with her work during an off the clock break, is that if the employer allowed this to happen, it would be liable for two or three times her wages for the period worked, regardless of whether the employee wanted to be paid. I think termination on the first offense is a little harsh (as did the state unemployment agency), but the employer was within its rights given that this situation has big implications for the workforce.
These situations are relatively rare, but the lesson should be reinforced--employees who work for you without recording their time, even voluntarily, are still adding compensable hours to their weekly totals, and must be paid for that time. Intent is not an issue here, but knowledge is. The employer must be aware of when its employees start and stop work in order to avoid double or triple back wage penalties under the wage and hour laws. This is a particular issue for employers that pay non-exempt employees a "salary"--if these folks are adding hours to their day by coming in early, staying late, or working during non-compensated time, then you have to increase their paychecks, including overtime, or risk an expensive visit from the DOL.