No, it wouldn't be oben either as that's used as an adverb, not a preposition, e.g. es ist oben = it's at the top. "She's at the top of the mountain", for example, would be "sie ist oben am Berg".
Which reminds me, "an" is another one of those prepositions that can take either the accusative or the dative. I can think of an, auf, in, hinter, über, unter, vor and zwischen but I'm sure there are more. As for why - to confuse us language learners even more? 
I still don't get the first and second object thing, though. If the man is the subject and the fox and dog are objects, they would both need to be in the accusative (or dative if indirect object) - the fox could only be der Fuchs if it's the subject of the the sentence.
The problem is that "the man, the fox and the dog" isn't a sentence - you need a verb to know what's going on. 
- All three nouns could be nominative, e.g. "Der Mann, der Fuchs und der Hund gingen spazieren."
- Or the man could be nominative but the fox and the dog accusative, e.g. "Der Mann sah den Fuchs und den Hund."
- Or you could have nominative, accusative and dative, e.g. "Der Mann gab dem Fuchs den Hund." (Or, like you say, "Der Mann sah den Fuchs mit dem Hund.")
That may all well be as clear as mud.
Must get back to German legalese, which is far less interesting!