syntactic analysis - Does being in the accusative case guarantee the existence of a direct object?

I want to clear this matter up once and for all. Even though I have already asked a few questions on the site related to the nominative case and the accusative case, I still get confused by one particular kind of example.

Let's take a simple sentence to consider my problem:

1. The book is on the desk.

According to the grammar book I am quoting from in the sentence I've just cited, desk is in the accusative case governed by the preposition on.

In the next exercise, there is a question which asks to find the object in this sentence:-

2. The boy stood on a burning desk.

I applied the same logic and thought that here burning desk must be the direct object since, as previously noted, it is in the accusative case governed by the preposition on.

But the book says that this sentence doesn't possess a direct object!

Is it because being in accusative case is different from forming a direct object, or is the "case" something else?

Please keep in mind that because I have only recently started studying basic grammar, that I will be unable to unravel extremely sophisticated, advanced analysis.