Additionally using mysqli_init() has the same behaviour.

# php -r '$mysqli = mysqli_init(); var_dump($mysqli->client_version); 
var_dump(mysqli_get_client_version());' ; mysql --version; php --version
int(50524)
int(50528)
mysql  Ver 14.14 Distrib 5.5.28, for Linux (x86_64) using readline 5.1
PHP 5.3.15 (cli) (built: Aug  9 2012 07:10:41) 
Copyright (c) 1997-2012 The PHP Group
Zend Engine v2.3.0, Copyright (c) 1998-2012 Zend Technologies
    with eAccelerator v0.9.6.1, Copyright (c) 2004-2010 eAccelerator, by 
eAccelerator
    with the ionCube PHP Loader v4.2.2, Copyright (c) 2002-2012, by ionCube 
Ltd., and
    with Zend Guard Loader v3.3, Copyright (c) 1998-2010, by Zend Technologies
    with Suhosin v0.9.33, Copyright (c) 2007-2012, by SektionEins GmbH

From Pierre Joye's twitter suggestion I add this info. I am using libmysql (no 
mysqlnd). It is the default shipped with cPanel in CentOs with easyapache 
script.

Some additional info:

# php -i | grep mysql

Configure Command =>  './configure'  '--enable-bcmath' '--enable-calendar' '--
enable-exif' '--enable-ftp' '--enable-gd-native-ttf' '--enable-intl' '--enable-
libxml' '--enable-magic-quotes' '--enable-mbstring' '--enable-pdo=shared' '--
enable-safe-mode' '--enable-soap' '--enable-sockets' '--enable-wddx' '--enable-
zend-multibyte' '--enable-zip' '--prefix=/usr/local' '--with-
apxs2=/usr/local/apache/bin/apxs' '--with-bz2' '--with-config-file-
path=/usr/local/lib' '--with-config-file-scan-dir=/usr/local/lib/php.ini.d' '--
with-curl=/opt/curlssl/' '--with-curlwrappers' '--with-enchant=/usr' '--with-
freetype-dir=/usr' '--with-gd' '--with-gettext' '--with-icu-dir=/usr' '--with-
imap=/opt/php_with_imap_client/' '--with-imap-ssl=/usr' '--with-jpeg-dir=/usr' 
'--with-kerberos' '--with-libdir=lib64' '--with-libexpat-dir=/usr' '--with-
libxml-dir=/opt/xml2' '--with-libxml-dir=/opt/xml2/' '--with-
mcrypt=/opt/libmcrypt/' '--with-mm=/opt/mm/' '--with-mysql=/usr' '--with-mysql-
sock=/var/lib/mysql/mysql.sock' '--with-mysqli=/usr/bin/mysql_config' '--with-
openssl=/usr' '--with-openssl-dir=/usr' '--with-pcre-regex=/opt/pcre' '--with-
pdo-mysql=shared' '--with-pdo-sqlite=shared' '--with-pic' '--with-png-dir=/usr' 
'--with-pspell' '--with-sqlite=shared' '--with-tidy=/opt/tidy/' '--with-xmlrpc' 
'--with-xpm-dir=/usr' '--with-xsl=/opt/xslt/' '--with-zlib' '--with-zlib-
dir=/usr'
mysql
MYSQL_SOCKET => /var/lib/mysql/mysql.sock
MYSQL_INCLUDE => -I/usr/include/mysql
MYSQL_LIBS => -L/usr/lib64 -lmysqlclient 
mysql.allow_local_infile => On => On
mysql.allow_persistent => On => On
mysql.connect_timeout => 60 => 60
mysql.default_host => no value => no value
mysql.default_password => no value => no value
mysql.default_port => no value => no value
mysql.default_socket => /var/lib/mysql/mysql.sock => /var/lib/mysql/mysql.sock
mysql.default_user => no value => no value
mysql.max_links => Unlimited => Unlimited
mysql.max_persistent => Unlimited => Unlimited
mysql.trace_mode => Off => Off
mysqli
MYSQLI_SOCKET => /var/lib/mysql/mysql.sock
mysqli.allow_local_infile => On => On
mysqli.allow_persistent => On => On
mysqli.default_host => no value => no value
mysqli.default_port => 3306 => 3306
mysqli.default_pw => no value => no value
mysqli.default_socket => /var/lib/mysql/mysql.sock => /var/lib/mysql/mysql.sock
mysqli.default_user => no value => no value
mysqli.max_links => Unlimited => Unlimited
mysqli.max_persistent => Unlimited => Unlimited
mysqli.reconnect => Off => Off
PDO drivers => sqlite, sqlite2, mysql
pdo_mysql
pdo_mysql.default_socket => /var/lib/mysql/mysql.sock => 
/var/lib/mysql/mysql.sock

# ldd /usr/local/lib/php/extensions/no-debug-non-zts-20090626/pdo_mysql.so
	linux-vdso.so.1 =>  (0x00007fffb9d03000)
	libmysqlclient.so.18 => /usr/lib64/libmysqlclient.so.18 
(0x00002ac356f05000)
	libm.so.6 => /lib64/libm.so.6 (0x00002ac357469000)
	librt.so.1 => /lib64/librt.so.1 (0x00002ac3576ed000)
	libdl.so.2 => /lib64/libdl.so.2 (0x00002ac3578f6000)
	libc.so.6 => /lib64/libc.so.6 (0x00002ac357afa000)
	libpthread.so.0 => /lib64/libpthread.so.0 (0x00002ac357e54000)
	/lib64/ld-linux-x86-64.so.2 (0x00000030ed200000)

Good find, must be a bug dating back years:

 OO interfaces uses compile time MYSQLI_VERSION
 Procedural interfaces uses run time C API function call

However, its slightly in the grey area. Client library version and server version are expected to match in general. AFAIK, in the past, only very conservative statements have been made about using library versions that differ from server version, particularily if using old library to connect to new server - which seems to be your case.

s/MYSQLI_VERSION/MYSQL_VERSION_ID

ext/mysqli/php_mysqli_structs.h:91:#define MYSQLI_VERSION_ID		101009
ext/mysqlnd/mysqlnd.h:26:#define MYSQLND_VERSION_ID 50011
ext/mysqlnd/mysqlnd_libmysql_compat.h:36:#define MYSQL_VERSION_ID		
MYSQLND_VERSION_ID

To clarify, this has nothing to do with the server (version); it's
rather about the difference of the version PHP (or the respective
extension) has been built against vs. which version is availble
during runtime.