For some reasons wiki pages are indexed with permissions only for admins when the project is private:
Test done with project "MV Valid 8.9" on https://c6.valid.enalean.com
When I'm searching as project admin everything works just fine but as a project member it fails
$ curl 127.0.0.1:9200/wiki/284/_search?q=new\&fields=page_name,permissions\&pretty
{
  "took" : 2,
  "timed_out" : false,
  "_shards" : {
    "total" : 1,
    "successful" : 1,
    "failed" : 0
  },
  "hits" : {
    "total" : 4,
    "max_score" : 0.5079906,
    "hits" : [ {
      "_index" : "wiki",
      "_type" : "284",
      "_id" : "22527",
      "_score" : 0.5079906,
      "fields" : {
        "permissions" : [ "@mv-valid-8-9_project_admin", "@mv-valid-8-9_wiki_admin" ],
        "page_name" : [ "new-page" ]
      }
    }, {
      "_index" : "wiki",
      "_type" : "284",
      "_id" : "22266",
      "_score" : 0.2073863,
      "fields" : {
        "permissions" : [ "@mv-valid-8-9_project_admin", "@mv-valid-8-9_wiki_admin" ],
        "page_name" : [ "AnalyseAccessLogSqlPlugin" ]
      }
    }, {
      "_index" : "wiki",
      "_type" : "284",
      "_id" : "22166",
      "_score" : 0.1693302,
      "fields" : {
        "permissions" : [ "@mv-valid-8-9_project_admin", "@mv-valid-8-9_wiki_admin" ],
        "page_name" : [ "UpLoadPlugin" ]
      }
    }, {
      "_index" : "wiki",
      "_type" : "284",
      "_id" : "22287",
      "_score" : 0.0846651,
      "fields" : {
        "permissions" : [ "@mv-valid-8-9_project_admin", "@mv-valid-8-9_wiki_admin" ],
        "page_name" : [ "PagePermissions" ]
      }
    } ]
  }
}