[Sync] Consolidate DataTypeController methods that post on the backend thread

tools/valgrind/memcheck/suppressions.txt

Index: tools/valgrind/memcheck/suppressions.txt
diff --git a/tools/valgrind/memcheck/suppressions.txt b/tools/valgrind/memcheck/suppressions.txt
index 8c061e2ffd90be28798427e758873112581a0aa0..f2e42bd217608522030f6829e22a96891347d4b2 100644
--- a/tools/valgrind/memcheck/suppressions.txt
+++ b/tools/valgrind/memcheck/suppressions.txt
@@ -4912,32 +4912,6 @@
    fun:_ZN11BalloonHost4InitEv
 }
 {
-   bug_105667_a
-   Memcheck:Leak
-   fun:_Znw*
-   fun:_ZN12browser_sync26TypedUrlDataTypeController21StartAssociationAsync*
-   fun:_ZN12browser_sync29NonFrontendDataTypeController5Start*
-   fun:_ZN12browser_sync19DataTypeManagerImpl13StartNextTypeEv
-   fun:_ZN12browser_sync19DataTypeManagerImpl13DownloadReady*
-}
-{
-   bug_105667_b
-   Memcheck:Leak
-   fun:_Znw*
-   fun:_ZN12browser_sync26TypedUrlDataTypeController20StopAssociationAsyncEv
-   fun:_ZN12browser_sync29NonFrontendDataTypeController4StopEv
-   fun:_ZN12browser_sync19DataTypeManagerImpl10FinishStopEv
-   fun:_ZN12browser_sync19DataTypeManagerImpl4StopEv
-   ...
-   fun:_ZN18ProfileSyncService8Shutdown*
-   fun:_ZN18ProfileSyncServiceD2Ev
-   ...
-   fun:_ZN22TestProfileSyncServiceD0Ev
-   ...
-   fun:_ZN10scoped_ptrI22TestProfileSyncServiceE5resetEPS0_
-   fun:_ZN30ProfileSyncServiceTypedUrlTest8TearDownEv
-}
-{
    bug_105715
    Memcheck:Uninitialized
    ...