Yes, it is. Át requires it, even as a prefix.
"Átmegyek az úton." -- "I cross the road."
This probably also applies to stepping on the stones if the river is shallow.
"Lép" means only one (1) step and my shoes won't get wet if "åtlépek" and not "àtgázolok" (cross a shallow river walking in the water). Átkelek, átmegyek - some more synonyms for crossing the river (by boat or through the bridge). The hidden meaning in Átlépek a folyón is that the river is too narrow.
Because there is no definite direct object.
The river is not an object (you don't "step the river") -- it's not in the accusative case.
We use: "Átlépek a folyón." - without any definite object but "Átlépem a folyót." is a valid translation, too.
I tried it first with a very direct translation :-) Through I step the river on ODER Durch schreite ich der Fluss auf. It is sometimes really difficult, to understand the grammar.
I cross over the river....... That should be a correct translation, shouldn't it?