As I understand it anyone with non PAYE income has to file a tax return. Revenue have decided that some people can do so by filing a Form 12. The circumstances are outlined at 4 below:
3. An individual with a PAYE source of income and with net assessable non-PAYE income (including income subject to DIRT) of €3,174 or more is regarded as a ‘chargeable person’ for Self-Assessment and must file a Form 11 for that year.
4. An individual with a PAYE source of income and net assessable non-PAYE income (due to losses, capital allowances and other reliefs) is less than €3,174 and the income is coded against PAYE tax credits or fully taxed at source, is not regarded as a ‘chargeable person’.
Unless your non resident landlord falls into the category 4. which may be difficult as they can't have the income coded into their tax credits they are a chargable person and have to file a Form 11.