In the select statement you'll use Verses.ID but in the array returned it will just be ID. The problem is that you have two three columns named ID. Select each using an AS to rename them so they are different.
$get_Event_sql = "SELECT Verses.ID AS versesID, Verses.Verse, Verses.Sub_Type, Verses.Event, Events.ID AS eventsID, Events.Event_Type, Event_Sub.ID AS event_subID, Event_Sub.Event_Sub_Type
FROM Verses
LEFT JOIN Events
ON Verses.Event = Events.ID
LEFT JOIN Event_Sub
ON Verses.Sub_Type = Event_Sub.ID
WHERE Verses.Event = '".$_POST["Event_Type"]."'
ORDER BY Verses.ID ASC";
Then it will be $row['versesID'] for the verses table ID.