This link stipulates that the 6th block on the PHP Information page (shown in your question) displays the path to the php.ini used by the Joomla installation.
Link: http://forum.joomla.org/viewtopic.php?t=350630
A good point mentionned again in the Joomla forum post from the link is that if you're on a shared host, you typically don't have access to the php.ini file. Still, someone mentionned this:
You can create php.ini at Joomla Directory. I do it usually.
Perhaps you can try that alternative? Is your public_html folder the top level Joomla installation folder?
EDIT: Someone mentionned that he had the same exact problem you have (upload size), and this is what he did:
I found that my host said that the php.ini need to be where the script was ran.
In this case for media manager it had a limit of 2mb.
Reason for this was uploading large files Acrobat PDF
I simply place a php.ini file into the administration folder of Joomla 1.5. Upon this PHP recognized the new php settings. Here are the php.ini file i created:
register_globals = Off
upload_max_filesize = 30M
post_max_size = 30M
memory_limit = 30M
upload_tmp_dir = 30M
max_execution_time = 180
Again coming from the Joomla forums post in the provided link. You can replace the 30M with whatever value you need.