Is the German sentence accurate? Do we not need a "gehen" or "kommen" for the main verb?
No, it's fine without a main verb. It's very common to omit the main verb after certain modals.
Here are some examples:
Ich kann Italienisch.
Ich soll dahin.
Wir müssen zurück.
... and, presumably, the famous "Hier stehe ich, ich kann nicht anders", with an implied "tun".
You should include this in the lessons. I can't recall from any lesson where this omission is mentioned.
If one can drop the verb, how is one supposed to know which verb to use? I tried "come" instead of "go" and it was not accepted. To me it makes as much sense to come back as to go back the same way. So, the question is: Why is only go allowed in the translation here?
What is wrong with "We can return the same way"? "go back" versus "return"?
I'm shocked no one has brought up the preposition "auf" which seems to have no real reason for being here. Anyway, after looking long and hard for a logical translation of this sentence, I've found that zurückgehen is an actual verb which means "to go back."
Knowing that along with what christian MOD said below, that it is common to omit the main verb after certain modals, the sentence makes complete sense in a colloquial way.
I think a literal translation, because of "auf," though, would be "We can go back on the same way."