> though there are no elements under
> <connectivity> which does not have an attribute with
> name  'sharedsource'

but that isn't what your xpath is testing.

connectivity/*[@*[not(local-name() = 'sharedsource')]]

selects all the elements that have an attribute whose name is not
'sharedsource'

they both have attribute of name id (for example) so they are both selected
and you get 2 elements.

You want

connectivity/*[not(@sharedsource)]

which says in Xpath what you said in english:
child elements of connectivity that don't have a sharedsource attribute.

David

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