I think that is exactly what they are saying, although perhaps "could be denied" rather than "would be denied". It is however contrary to the following statement from the UAE Embassy in the US with respect to US citizens and "non-US citizens from certain countries (which hopefully reflects the current policy): "Visas are available upon arrival to the UAE airports, This includes those who hold visas in their passports or entry stamps from other countries and visa is valid for one (1) month stay in the UAE." (My emphasis).

The way I read that statement, it means that the UAE could care less what visas or stamps are in your passport. Having another country's visa or stamp, or none, has no bearing on whether or not a UAE visa is issued. YMMV.