Fatal error : allowed memory size exhausted

Does disabling this module solve your problem?

Sorry I don't understand the problem.

This module only adds one permission to that list - I don't think it should cause this problem.
You don't have any other output on the page that could add to the memory? Often a giant drupal_set_message or another piece of themed output like a block will cause this.

Hallo,
Try to increase your php memory limit. There are many ways to do that, here is a quick one:
in your settings file, add:

ini_set('memory_limit', '48M');

^ good idea, I've had to do this on most of my sites for other reasons anyway.

Strangely, I have the same issue.

When I access the node edit page,
as an user who should have the edit permission granted through this module, I get a blank page.

The error message below is generated by the error log of my local server, running under php 5.3.2
(Running with php 5.2.13 get no error at all)

PHP Fatal error: Allowed memory size of 33554432 bytes exhausted (tried to allocate 243 bytes) in /Applications/MAMP/htdocs/mydrupalsite/sites/all/modules/nodeaccess_nodereference/nodeaccess_nodereference.module on line 250

However, the memory seems to be no problem.

If I access the page as master admin I can see the site properly,
as I already have the appropriate permissions granted through drupal core, I guess.

Any clue how this issue could be solved?

According to the error log, the error is happening here:

    if (!empty($ops)) {
      $do = implode('/', $ops);
      switch ($row->realm) {
        case 'nodeaccess_userreference':
          $account = user_load(array('uid' => $row->gid));
          return t('Referenced user %name may !do this node', array('%name' => $account->name, '!do' => $do));
        case 'nodeaccess_userreference_author':
          $account = user_load(array('uid' => $row->gid));
          return t('Node author %name may !do this node', array('%name' => $account->name, '!do' => $do));
        case 'nodeaccess_userreference_all':
          return t('All users may !do this node', array('!do' => $do));
      }
    }

Ok, sorry. It was a stupid issue.
The problem actually was rooted at: Node access node reference.

The page had a node reference referencing to itself.
This generated a loop.

Thank you for this great module!!