Looking in the sources, 1 second is used (the "unix" granularity) instead of the claimed 0 milliseconds.

git-svn-id: https://svn.apache.org/repos/asf/ant/core/trunk@277275 13f79535-47bb-0310-9956-ffa450edef68

docs/manual/CoreTasks/copy.html

@@ -133,7 +133,7 @@ operation as <a href="../CoreTypes/filterset.html">filtersets</a>
     <td valign="top">The number of milliseconds leeway to give before
     deciding a file is out of date. This is needed because not every
     file system supports tracking the last modified time to the
-    millisecond level. Default is 0 milliseconds, or 2 seconds on DOS
+    millisecond level. Default is 1 second, or 2 seconds on DOS
     systems.  This can also be useful if source and target files live
     on separate machines with clocks being out of sync.  <em>since Ant
     1.6.2</em>.</td>

src/main/org/apache/tools/ant/taskdefs/Copy.java

@@ -343,8 +343,9 @@ public class Copy extends Task {
      * The number of milliseconds leeway to give before deciding a
      * target is out of date.
      *
-     * <p>Default is 0 milliseconds, or 2 seconds on DOS systems.</p>
-     *
+     * <p>Default is 1 second, or 2 seconds on DOS systems.</p>
+     * @param granularity the granularity used to decide if a target is out of
+     * date.
      * @since Ant 1.6.2
      */
     public void setGranularity(long granularity) {