I am not sure about what notices auDA had sent, but I can say that this is a
common issue in the doman name industry.  There are often mutiple entities
which could have a trademark relating to a domain name.  I believe that
trademarks can be registered in about 42 categories, thus two companies
could have the same trademark but operate in different industries.

When you register a domain name, the terms and conditions of registration
usually have a statement such as the following:
"The Licensee warrants that neither the registration of the Domain Name nor
the manner in which the Domain Name is directly or indirectly used infringes
the legal rights of a third party. "

Then there is a dispute reslution mechanism that can be used instead of the
courts for a person or company to claim that the registrant of a particular
name is using it in bad faith.  These dispute resolution mechanisms (called
UDRP for gtlds, or auDRP for ".au" domains) are intended to reduce the cost
for a third party to have a domain name revoked from a company that is using
it in bad faith.

Regards,
Bruce Tonkin