The privilege for voting to close and reopen posts on private beta sites is supposed to be given out at 1 reputation, and for a while, it was. However, at some point, a bug was introduced: basically, close votes were refactored internally to be stored as flags (to allow users without close-voting privileges to cast "recommend closure" flags), and as the flagging privilege is not given out until 15 reputation, users with less than that became unable to cast close votes.
This creates a confusing scenario: the
/privileges page says that a 1-rep user has the vote-to-close privilege, but they actually can't make use of that privilege until they have 15 rep, due to a bug in internal code.
What's that "internal code"? Well, according to the answer to a recent bug report reporting a related issue, the check for actually being able to vote to close checks for both flagging and closing privileges, and if the user doesn't have flagging privileges, it flatly assumes they don't have closing privileges either and doesn't allow the user to vote to close.
This is an inconsistency, and should be fixed. But I'm not sure how we should go about fixing it. Should we fix the bug directly and return to the original behavior of allowing 1-rep users to vote to close posts, or should we increase the privilege level to 15 rep?
In my opinion, we should opt for the latter, because back when the privileges were originally structured, only committers could access the site, which meant that the users already sort of knew what was on- and off-topic for the site as they participated in the proposal, so it made sense to give out closing privileges to all users. However, these days, anyone can access a private beta site (provided they go through the proposal page), so it might be worth requiring minimal experience in the site before they can decide what's on- and off-topic. Also, the answer to that bug report says that increasing the privilege level to 15 rep is a slightly simpler fix.