The full patch:

diff --git a/tomcat6-6.0.init b/tomcat6-6.0.init
index 3d59e7b..a1e7e83 100644
--- a/tomcat6-6.0.init
+++ b/tomcat6-6.0.init
@@ -66,6 +66,9 @@ TOMCAT_PROG="${NAME}"
 # Define the tomcat username
 TOMCAT_USER="${TOMCAT_USER:-tomcat}"

+# Define the tomcat group
+TOMCAT_GROUP="${TOMCAT_GROUP:-tomcat}"
+
 # Define the tomcat log file
 TOMCAT_LOG="${TOMCAT_LOG:-/var/log/${NAME}-initd.log}"

@@ -122,7 +125,7 @@ function start() {
     # fix permissions on the log and pid files
     touch $CATALINA_PID 2>&1 || RETVAL="4"
     if [ "$RETVAL" -eq "0" -a "$?" -eq "0" ]; then
-      chown ${TOMCAT_USER}:${TOMCAT_USER} $CATALINA_PID
+      chown ${TOMCAT_USER}:${TOMCAT_GROUP} $CATALINA_PID
     fi
     if [ "$?" != "0" ]; then
        RETVAL="4"
@@ -200,7 +203,7 @@ function status()
       if [ "$RETVAL" -eq "2" ]; then
          log_failure_msg "${NAME} lockfile exists but process is not running"
       else
-         pid="$(/usr/bin/pgrep -u ${TOMCAT_USER} -f ${NAME})"
+         pid="$(/usr/bin/pgrep -d , -u ${TOMCAT_USER} -G ${TOMCAT_GROUP} java)"
          if [ -z "$pid" ]; then
              log_success_msg "${NAME} is stopped"
              RETVAL="3"
@@ -215,7 +218,7 @@ function status()
 function checklockfile()
 {
    if [ -f /var/lock/subsys/${NAME} ]; then
-      pid="$(/usr/bin/pgrep -u ${TOMCAT_USER} -f ${NAME})"
+      pid="$(/usr/bin/pgrep -d , -u ${TOMCAT_USER} -G ${TOMCAT_GROUP} java)"
 # The lockfile exists but the process is not running
       if [ -z "$pid" ]; then
          RETVAL="2"
@@ -230,6 +233,7 @@ function checkpidfile()
       if [ -d "/proc/${kpid}" ]; then
 # The pid file exists and the process is running
           RETVAL="0"
+         return
       else
 # The pid file exists but the process is not running
          RETVAL="1"

The patch will solve the problem, but there's another one:
pgrep will catch all java processes running as user tomcat and group tomcat. So, if no PID file is available, you will not get the PID of your instance, but all running tomcat PIDs.

I think that the last directory of $CATALINA_BASE should be identical to the instance name $NAME, otherwise there's no chance to determine the correct PID if no PID file is available.

Assuming that the last directory of $CATALINA_BASE is the instance name ${NAME}, we can use pgrep with $NAME as the pattern.
The problem is: pgrep matches all processes that have the given pattern anywhere in between.
Example: You have two tomcat instances, tomcat6-custom and tomcat6-custom2.
A "service tomcat6-custom status" will return 2 PIDs, because pgrep matches both processes.

To solve this problem, I have replaced both occurences of pgrep:
-pid="$(/usr/bin/pgrep -u ${TOMCAT_USER} -f ${NAME})"
+pid="$(/usr/bin/pgrep -u ${TOMCAT_USER} -fx .*${NAME}\ .*)"

pgrep -x does an exact match.

Since the problem described in this bug report should be
resolved in a recent advisory, it has been closed with a
resolution of ERRATA.

For information on the advisory, and where to find the updated
files, follow the link below.

If the solution does not work for you, open a new bug report.

http://rhn.redhat.com/errata/RHBA-2013-1721.html