I examined the http://fdsrv.fire-defence.com/editordemo.aspx page and found that the editor in it is rendered with div content area mode.
I am not sure what do you mean by the name Richtext editor, but if you are using the same editor (RadEditor for ASP.NET AJAX) as the one of the former link, you can turn its content area to DIV by setting ContentAreaMode="Div" and retest.
This jQuery code also does not use the RadEditor's API to catch the pasted content
$(this.editor.get_document()).on("paste", $.proxy(this.handlePaste, this));
and my advice is to not use it but use the OnClientPasteHtml event to capture the content.
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