People will, as always, interpret this Danish study in whichever way suits their ideological beliefs. However, let me point out that, ideology aside, it is possible for a population to both be a net fiscal negative and yet have a positive influence on the economy.
An extreme instance of this is in slave societies. Slaves don't pay taxes and therefore are a net negative fiscally. Yet the taxes slave owners pay are largely drawn from slave labour and in fact the economy is essentially reliant on the slaves' work.
Likewise, it is possible that immigrants take on low-skilled, low-paid jobs, which are essential to the economy despite not directly contributing fiscally. This then could free the natives to perform more lucrative jobs and thereby contribute more than if immigrants were not there.