I have only seen people buying puts to go short and in that case you do not pay the dividend. Also, the exdivy date should be a non event. The stock goes down the same amount as the dividend paid so whether a short covered the day before or the day after it would make no difference to them.
In the long run I would say a short would lose money on a stock that pays such a high dividend so long as the stock price does not vary too much and so I can only imagine that they are trading short term because they think they have observed a trend that repeats quarterly and they are trying to exploit that trend. In that case they are usually leveraged with options so they can get the biggest bang for the buck.
I cannot fault this investment approach but it is not what I do. I simply own the stock and allow the dividend to accumulate. But I cannot find fault with the short term trading approach either. It seems to be working for many so long as you know what you are doing.