I think you're misinterpreting that. Everything other than food and fuel went up 2.8%. Everything (including food and fuel) went up 3.8%. Therefore food and fuel went up more than 3.8%.
We can see that advertised on every corner, too. Gas costs for me locally went from $3 pre-war to over $5 now. My "investment" in EVs and solar is feeling really good right now.
You have food and fuel, which is some fraction of the economy - call that F. You have a rate of inflation in fuel and food - call that f. And you have a rate of inflation in everything else - call that e. Then you have
3.8 = e(1-F) + fF.
You also have e = 2.8.
I think what you're claiming is that fF = 1.0, so that e(1-F) = 2.8. And I think that's wrong. When they say inflation apart from food and fuel is 2.8, they mean e, not e(1-F).
You're over complicating it because you don't need rates within subcategories when looking at the whole - e is given and f is useless.
3.8 - 2.8 = 1
The overall inflation is 3.8. Overall inflation without food and fuel is 2.8. The overall inflation attributable to food and fuel must then be 1 (this is different than rste of inflation within food and fuel as a category, f).