It's not just approximately shown; the keys documentation explicitly says that (so long as it's not modified) they will return the same order for the same hash (emphasis mine):

Hash entries are returned in an apparently random order. The actual random order is specific to a given hash; the exact same series of operations on two hashes may result in a different order for each hash. Any insertion into the hash may change the order, as will any deletion, with the exception that the most recent key returned by "each" or "keys" may be deleted without changing the order. So long as a given hash is unmodified you may rely on "keys", "values" and "each" to repeatedly return the same order as each other.