What they say seems correct.
You are a "British citizen by descent", because you were automatically a British citizen at birth due to being born outside the UK to a parent who was a British citizen otherwise than by descent. It doesn't matter what they did or did not do after your birth; you are still a British citizen by descent. You cannot "upgrade" yourself to "otherwise than by descent".
Your children born abroad are not automatically British citizens at birth, because that can only happen if they have a parent who is a British citizen otherwise than by descent. I am guessing that their only British-citizen parent is you, who is by descent. In other words, automatic transmission of British citizenship at birth outside the UK only extends one generation.
Your children may be eligible to register to become British citizens after birth, while under 18, in one of the following cases:
- Section 3(2): The parent who is a British citizen by descent (you) must have lived in the UK for any continuous period of 3 years before the child's birth, during which you were not absent from the UK for more than 270 days. This period of 3 years does not have to be recent; it could be from your childhood. If your children are registered under this section, they are considered "British citizens by descent".
- Section 3(5): Both parents and the child have lived in the UK for the 3 years immediately before you make this application, during which you were not absent from the UK for more than 270 days. If your children are registered under this section, they are considered "British citizens by registration". But this would only be possible if you plan to move to the UK for a few years.
- Section 3(1): At the Home Secretary's discretion. This is very unlikely unless the children have a special connection to the UK or something.
Really though, if you have not lived in the UK for 3 years in your life (to qualify under section 3(2)), then your children's connection to the UK is pretty distant and it is reasonable for them to not be British citizens. Even if they are not British citizens, I believe they can still go to the UK on the Ancestry Visa.