As a long time low-carb dieter, I have never found that the ketosticks would change color, unless I was doing my low carb regimen. I am not sure about the ketosticks showing fat that you have just eaten.
A few years back, just for the **** of it... I would go to a big barbeue and eat my typical share of hamburgers, ribs, chicken... etc..... and then I would test for ketones several times that night... and there was NEVER any indication of ketones.
I am not saying this isn't true about what you've eaten not affecting the reading, I am merely saying I have never, in my experience, found this to be the case.
Good luck!!! Since your losing inches, you are having some success.