Index: src/bp-groups/bp-groups-filters.php
===================================================================
--- src/bp-groups/bp-groups-filters.php
+++ src/bp-groups/bp-groups-filters.php
@@ -232,6 +232,9 @@
 				break;
 			}
 
+			// Set to false to begin with.
+			$retval = false;
+
 			/*
 			* The group must accept membership requests, and the user should not
 			* currently be a member, have an active request, or be banned.
Index: tests/phpunit/testcases/groups/user_can.php
===================================================================
--- tests/phpunit/testcases/groups/user_can.php
+++ tests/phpunit/testcases/groups/user_can.php
@@ -368,4 +368,24 @@
 		$this->assertTrue( bp_user_can( $u1, 'groups_see_group', array( 'group_id' => $g1 ) ) );
 	}
 
+	/**
+	 * @ticket BP7610
+	 */
+	public function test_user_can_groups_request_membership_for_super_admin() {
+		if ( ! is_multisite() ) {
+			return;
+		}
+
+		$g1 = $this->factory->group->create( array(
+			'status' => 'public'
+		) );
+		$u1 = $this->factory->user->create();
+		$this->add_user_to_group( $u1, $g1 );
+
+		// Grant super admin status.
+		grant_super_admin( $u1 );
+
+		// Assert false since public groups shouldn't be able to request membership.
+		$this->assertFalse( bp_user_can( $u1, 'groups_request_membership', array( 'group_id' => $g1 ) ) );
+	}
 }