The difference is not in what is being done, but in who is in charge.
If you modify your router settings, it's you. You decided that you are not going to honor ISP suggested defaults, and it is up to you to assess costs/benefits and pick the right choice.
If Firefox overrides your settings, it means someone else does the decision about your tools. If that someone else makes it difficult to automate changing the default (e.g. ignoring DHCP; if you want, you can ignore DHCP at the system level, but this is not a decision an app should take), it means, that this someone else doesn't have good intentions towards you. Someone else decided what's "best" for you.