Plain wire is also a resistor,
Yes, but it has a resistance of 0.000 Ohm.
And the SMD resistors do not have such low resistance.
Aside from superconducting materials at very low temperatures - everything has resistance. 0-ohm SMD resistors are simply guaranteed to be lower than a certain threshold with little regard to accuracy.
Just because something has "000" on it doesn't necessarily mean "0.00" and even if it did it gives no indication of accuracy. Most likely they are manufactured the same way other resistors are, and those have a 3-digit code. So rather than change the manufacturing to only print one digit "0" they print three.
Also, don't confuse accuracy, with precision, or tolerance. There are different concepts. Often values are printed with far more decimal points than is possible to measure accurately, usually because figures are generated with a certain number of digits, say 3 decimal places, even when the measurement accuracy is terrible. eg 1.446 +/- 0.5 should be to one decimal place -> 1.5 +/- 0.5.
This misunderstanding may seem insignificant but I have known designers to assume builders work to sub milliliter accuracy because their software uses figures to several decimal places.
I'm intrigued - do you think that all 10k resistors have exactly 10.000k ohm? And how accurately you can measure things is down to how accurate your equipment is - and again we bumped into the difference between accuracy, precision and tolerance.
https://meettechniek.info/measurement/accuracy.html