not AT ALL true
slaves do not get a salary, but they DO require not insignificant maintenance costs - food, clothing, housing, medical care (at least what is required to keep them alive and capable of work), etc etc etc
If your arrangement is one where your monetary outlays on your slaves are LESS than what your purchase price and maintenance costs would be, then you do still effectively own slaves, but your ownership is implied instead of direct, and your long-term capital commitments and risks are MUCH much lower.
I much prefer the slave system we have now as opposed to the ones we have had in previous eras. I would much rather have it this way than to have to directly buy and maintain my own slaves