And you're interpreting the chief as a one trick pony, as it were. Just because all we've seen is one trick does not make him incapable of others. The absence of an eye in the sky figure (indeed, there isn't an absence, in the form of Cortana) is no more a prescription to run in circles than seeing an unoccupied tank is a prescription to massacre friendlies. Could you do it? Yes. Would you do it? If you're that special kind of crazy, yes. Is it the logical conclusion? No.
Spartans, by all in-game, in-fiction, and other in-universe accounts, specifically excel at vague direction low profile operations. This fits the bill to a t.