Here is how my Mazda looks like under the trunk area. It was sprayed with Krown for 5 years, but I skipped the application for the last two years. I will do it this year though. Fluid Film would be very similar.
As you can see the cross member looks pretty dry, but that's because it's a high wash area and it's covered in dirt, as we had quite a lot of construction in the past (that's the reason I didn't rustproof as it would just get covered in mud), but there is still some oil left there.
The trunk area is still wet and over the years it just becomes almost like black tar from all the dirt sticking to it. If you touch that you will get dirty.
However, for most routine stuff I hardly ever get dirty from touching the treated areas. The engine and transmission are not treated, so changing these fluids is no big deal. Same thing with brakes because only suspension arms are sprayed, but even then, because those are high wash areas, they don't stay as wet and dirty as the main body of the car.
For all other stuff where you have to touch those very dirty areas, they can be easily wiped with some rugs and then re-treated.
Edit:
And let's face it, working on cars, especially few years old with some miles under their belts, is a dirty business any way. I have my working cloths for this very reason and lots of hand washing soap. But one thing is for sure, I'd rather get a bit more dirty than spend several hours working on something that normally would've taken 30 minutes just because a rusty bolt snapped off on me.