The Mozilla Corporation wants Ubuntu and Debian to use the Firefox name and logo correctly, and to run custom patches by Mozilla Corp. before including them in their distributions. Naturally, this makes the process of updating the program harder, and it will be a lot more time consuming to include custom patches for these distributions.
Ubuntu and Debian's position is certainly understandable since it creates more work for them, but some of the criticizm against Mozilla regarding this matter seems to be a bit rash.
If I am not mistaken, a trademark is lost if one does not protect it. This means that anyone can create "Firefox" and distribute it as such. The logo itself is covered by copyright which cannot be lost anyway, but the value of having only one official version of a program to relate to is not to be underestimated. (Please correct me if I'm getting anything wrong here.)
Think of a scenario where everyone can create a product like yours and put your name and logo of it. Theirs is a cheap ripoff which gives your trademark and logo a bad reputation. Does that sound nice to you?
Mozilla Corp. is protecting its trademarks and logos because it benefits them (users use their products rather than products pretending to be theirs), and it benefits the users (users know that what they are using is an official Mozilla Corporation product, so they know who is responsible for it).
Now, I am not saying that Ubuntu or Debian would give Mozilla a bad name – not at all. The scenario I mention above is purely hypothetical, but I still believe that this is closer to the reason why Mozilla Corp. is doing this than the various conspiracy theories about how Mozilla Corp. is turning into Microsoft and similar remarks from around the Web…
In the end, Mozilla Corp., Ubuntu and Debian may come to an agreement on how to handle this. Maybe Mozilla will be able to give special permission in some cases, or maybe the two Linux distributions will eventually sympathize with Mozilla Corp.'s position and find a way to handle it anyway.
Protecting a brand is beneficial to the owner of the brand as well as the users/customers, so it is no wonder that Mozilla Corp. takes steps to ensure that their brand is kept intact and exclusive.