Only set precache.last_time when precache ran.

components/precache/content/precache_manager.cc

Index: components/precache/content/precache_manager.cc
diff --git a/components/precache/content/precache_manager.cc b/components/precache/content/precache_manager.cc
index f3f2efce9ec60bbebe419290cb22d23426e1c935..60a2742efcc8609361949cc9303874cc6a082bd8 100644
--- a/components/precache/content/precache_manager.cc
+++ b/components/precache/content/precache_manager.cc
@@ -96,11 +96,11 @@ void PrecacheManager::StartPrecaching(
                      "in progress.";
     return;
   }
-  is_precaching_ = true;
-
   precache_completion_callback_ = precache_completion_callback;
 
   if (ShouldRun()) {
+    is_precaching_ = true;
+
     BrowserThread::PostTask(
         BrowserThread::DB, FROM_HERE,
         base::Bind(&PrecacheDatabase::DeleteExpiredPrecacheHistory,
@@ -187,15 +187,13 @@ void PrecacheManager::Shutdown() {
 void PrecacheManager::OnDone() {
   DCHECK_CURRENTLY_ON(BrowserThread::UI);
 
-  // If OnDone has been called, then we should just be finishing precaching.
-  DCHECK(is_precaching_);
-  is_precaching_ = false;
-
   precache_fetcher_.reset();
 
-  precache_completion_callback_.Run();
+  precache_completion_callback_.Run(is_precaching_);
   // Uninitialize the callback so that any scoped_refptrs in it are released.
   precache_completion_callback_.Reset();
+
+  is_precaching_ = false;
 }
 
 void PrecacheManager::OnHostsReceived(