It's impossible for me to know who actually said what. However, the fact that the initial Twitter handle included the company name - @Phonedog_Noah - gives PhoneDog every right to claim it. Why they chose to sue many months later and how they calculated the dollar amount are separate issues.
If your Twitter handle contains your company name, it's no longer yours. Yes, you probably still include personal tweets and showcase your own wit and humor, but that's par for the course on Twitter. An organization wouldn't have hired someone to run a social media feed – I hope – unless they possessed that unique aptitude necessary for succeeding in an online world.
There are plenty of cases where an individual at a company has made a name for themselves while giving a voice and human face to a brand on Twitter. Best Buy, Ford, and Southwest Airlines all come to mind. But Frank Eliason, who ran the @ComcastCares Twitter account for years, is probably the best example. When Eliason left Comcast for Citi last year, he didn't try to take @ComcastCares with him. He promptly opened a @FrankEliason account, and a gentleman named Bill Gerth and employed by Comcast took over ComcastCares.
Why an employee would want to solely tweet for their employer just doesn't make sense in this age of personal brand. True, it takes time to maintain both a personal and professional Twitter feed, but that's just the reality if your job includes social media and you want to avoid Kravitz's fate.
This case shows the confusion and complications that continue to arise from social media for both employees and employers. The bottom line is that someone wasn't clear on the company policy – whether that was the employee or the employer, I don't know. It serves as a great lesson for all organizations to review their social media policies with employees.