File Upload to SharePoint 2013 using REST API fails with code:"-2147024891, System.UnauthorizedAccessException

I have developed this code

$spSiteUrl = "http://mysharepoint/sites/site/web"
$cmd = "_api/web/lists/getbytitle('$docLib')/rootfolder/files/add(url='" + $file.Name + "', overwrite=true)"
$digest = "got valid digest through code";
$mediaType = new-object("System.Net.Http.Headers.MediaTypeWithQualityHeaderValue") "application/json"
$handler = new-object("System.Net.Http.HttpClientHandler")
$handler.UseDefaultCredentials= $true
$client = New-Object("System.Net.Http.HttpClient") $handler        
$client.BaseAddress = $spSiteUrl
$client.DefaultRequestHeaders.Accept.Clear()    
$client.DefaultRequestHeaders.Accept.Add($mediaType);
$client.DefaultRequestHeaders.Add("Accept", "application/json;odata=verbose")
$content = $null
$client.DefaultRequestHeaders.Add("X-HTTP-Method", "PUT")
$client.DefaultRequestHeaders.Add("X-RequestDigest", $digest)
$fileStream = [System.IO.File]::OpenRead($file.FullName)
$streamContent = new-object ("System.Net.Http.StreamContent") $fileStream
$task = $client.PostAsync($cmd, $streamContent)
$response = $task.Result
$content = $response.Content.ReadAsStringAsync().Result
Write-Host $content
$fileStream.Close()
$fileStream.Dispose()
$response = $response.EnsureSuccessStatusCode()
$client.Dispose()

Here I have a valid digest value which I got from doing a POST on _api/contextinfo.

However when I run this code, I get an error 

{"error":{"code":"-2147024891, System.UnauthorizedAccessException","message":{"lang":"en-US","value":"Access denied. You do not have permission to perform this action or access this resource."}}}

_api/web/lists/getbytitle('test')/rootfolder/files/add(url='BaselineFinishTag_2014_06.log', overwrite=true)

I am the site collection owner and also farm administrator. The code is being executed by my account and as you can see that I am using UseDefaultCredentials=true. So why does this code not work?

Edit:: Could it be my age old nemesis the "Authorization" header with Bearer and AccessToken? But this is a powershell script so ofcourse there is no TokenHelper class which will provide me an AccessToken.

val it: unit=()