SAT® tense: simple past or past perfect?

[Ecoke0005]

Hi guys.
please help me out with the following question.

Shortly after (arriving) at the amusement park with the eager third graders, the parents (realized) that they had brought (nowhere near) the (number) of chaperones required to control the children. No error.

right answer is: (nowhere near) because it is unconventional use.

But isn't the use of (arriving) also wrong here? shouldn't it be (having arrived) using the past perfect tense since "arriving" occurred before "realizing"? I understand that "simple past" can replace "past perfect" in some occasions when used with "after" or "before." But this mixed use of both tense really confuses me. Can anyone please explain this to me?

thank you.