In principle you are perfectly right.
Which country are you in?
For example in Germany, a dividend received by a fund and reinvested within the fund (hence never distributed to the investor) is taxed the same as a distributed dividend (*). That means that you often need to declare it in your tax return (usually not necessary for distributed dividends since those will be taxed automatically as they are paid to you) and you actually need to have the money to pay the ensuing tax bill.
This tends to make reinvesting funds a bit of an administrative headache in Germany. It's not really bad, you understand, but it is more complicated than with a distributing fund.
(*) I am wondering how this is in other countries. Where are all of you, and do you have to pay taxes on reinvested dividends in the year in which the fund reinvests them? [shimrod, if you think this takes this thread too much off-topic, please just tell me and we will move this question to another thread]