The template itself is - hence calling (Template:="lalala.doc")

If I call a *.dot file, it will open the template itself, rather than a file based on the template.

I've just tried it though:
Set myDoc = wdApp.Documents.Open "H:\Storage\My Documents\7 - Training\Forums\ExWd.doc"
and
Set myDoc = wdApp.Documents.Open "H:\Storage\My Documents\7 - Training\Forums\ExWd.dot"
, just in case! Still, no go!