Your accountant is right that all property owners, whether legal residents or not, must pay annual taxes on
bienes personales. Residents pay 0.50 - 1.25% of the total value of holdings on 12/31 of each year. Non-residents (i.e. those without a DNI) pay a flat rate of 1.25% of the total value. but, of course, they're not required to pay taxes on property outside Argentina, which residents are required to declare.
Just to clarify, the exemption amount, currently $305.000, does not reduce the taxable base. For example, if you own personal property valued at $400.000, tax is due on $400.000, not on $95.000. On the other hand, if the total value of your personal property is $300.000, then NO taxes are due. (These values are all in pesos.)
The $305.000 exemption applies equally to residents and non-residents.
Fyi, here's the tax rate chart from AFIP's English-language pages at
http://www.afip.gob.ar/english/about.asp.
. Amount . Tax rate
FROM $ 305.000 THROUGH $ 750.000 . 0.50%
FROM $ 750.001 THROUGH $ 2.000.000 . 0.75%
FROM $ 2.000.000 THROUGH $ 5.000.000 . 1.00%
FROM $ 5.000.000 ONWARDS . 1.25%
I have a call in to my accountant regarding CarverFan's original post. I will post more info when I hear from her.