The derailleur and cassette are compatible; in the sense that they will work together when they are installed on your bike, and the derailleurs are adjusted correctly.
Shimano states them to be incompatible, but this is not to say they would not function; rather they would not function as Shimano intended them to. This is because Shimano designs their drivetrains as a set, rather than individual components.
In the case of the 7900 cassette and 7800 derailleur with 53-39 chainrings, it should function , based on details that are not part of the derailleur design. Such as if you know how to shift through your gears correctly. If you shift into the largest chainring, and then onto the 28t rear cog, there is a chance that the drivetrain could bind. This is based on things like chain length, chainstay length, rear dropout design, and how far the B-tension screw is turned in on the derailleur. Since Shimano can't control these aspects of your riding experience, they simply state that the two components are not compatible.
My professional recommendation to a customer who wanted to use the 11-28 cassette, but didn't want to buy a new derailleur would be this:
- Install the cassette and derailleur.
- Measure your chain to the correct length (using Park Tool's 3rd method), but do not cut the chain yet.
- Add an additional link (outer/inner) to the total chain length.
- Cut the chain, install, and check the shifting function.
- Adjust the B-tension screw in on the derailleur so that the chain and upper jockey wheel on the derailleur do not grind against the largest rear cog.
If for some reason you can't adjust the drivetrain noise out, then forget it. Any of the above factors may make it impossible. It's unusual, but it does sometimes happen. If there is excessive slack in the chain in the small ring/small cog combination, it's also probably not a great idea. However, I would not worry a great deal; Shimano SS cages have never been compatible with 28t cogs, but tons of people run them all the time. It's for legal protection that Shimano states this. What you really need to run an SS cage and a 28t cassette is mechanical know how (or a good shop mechanic!)