No, not all homes are eligible for a reduction via the Rent Tribunal. Homes above the liberalization limit (the limit between social rented homes and private rented homes) cannot be lowered. However, it sometimes happens that an independent home actually belongs in the social sector after a scoring (rent check) has been done. This can be done within the first six months after signing your rental contract.
Example: Charlie lives in a small apartment and pays 1050 euros basic rent here. After a rent check, it appears that the house should have been only 590 euros. Charlie has been living here for five months. Despite the fact that the house is rented out in the private sector, the Rent Tribunal can still lower the basic rent.