Re: IE seems unable to 'GET' PIE.htc from my site
When working with .htc files and SharePoint 2010 (and any version of IE after IE7), you must either be in Permissive File mode or add the "text/x-component" MIME type to the "AllowedInlineDownloadedMimeTypes" list for each web application using PIE.
Permissive mode is the easiest to set on a web app but also opens you up to potential exploits if you allow users to upload content. (This is the same reason why PDFs do not open inside your browser by default in SharePoint 2010)
If this MIME type is not allowed, then IE will download the .htc but it will refuse to execute any behaviors contained in the file (the file is sent with the "X-Download-Options:noopen" header).
Adding the mime type to the webapp is relatively simple via PowerShell.
$webapp = Get-SPWebApplication <name or URL of web app>
This is a per-webapp setting, so you will need to make the change to each webapp that will use PIE.
Making this change will also let you store the PIE.htc inside a document library.