Dividends don't perfectly reflect a stock price drop, but to say they're unrelated isn't correct either. It's easy to see if you imagine an extreme example. Company A has no dividend, Company B pays a 20% dividend every year. They both have a profit of 20% per year. Assuming both companies have the exact same amount of sales, cash flow, expenditures, and are exact mirrors of each other, you're telling me their prices should still be about the same on the market. The thing that will drive them apart is that while Company B is paying out all of its profits to shareholders, Company A is using that money to grow its business in a way Company B can't match. Eventually, assuming they are both decent companies whose investments make them money, Company A will grow much larger than Company B, and the stock price will reflect that. The flip side to this is, if you reinvest the dividend from Company B into its own stock, you should see the exact same overall profit (neglecting taxes).
Obviously there is noise in the real world. The question is, do you trust leaving your money with the company, or would you rather they give it back to you (so you can then give it back to them through reinvestment...). Dividends can help keep a company accountable to shareholders, as it's a certain amount of money they have to give shareholders instead of using it on a crazy scheme just because they don't know what else to do with it.
Would you rather have 1 share worth $100 or 2 shares worth $50?
For an individual stock there is enough noise in the price that a dividend won't affect it as much as everything else. So it's true that if you pick one stock and look before and after the dividend it could've gone up or down. I suspect if you looked at 100, 200, 500 stocks to average out the noise, there would be an overall pattern consistent with the theory. The other complicating factor is that often dividend and non-dividend stocks are in different industries, thus comparisons become even more tricky.