Well, that's one of the reasons demonstrating the Meissner effect is considered a better evidence of superconductivity. Of course any physical experiment always has a noise floor and a finite error. You can't exactly ever measure zero resistance because your probes and the probe-sample interface have nonzero resistance…
But looking at that graph, it would be an incredible coincidence if the resistance dropped like it does and then suddenly stabilized to some very small but nonzero value… That would probably require entirely new physics to explain and would be a much bigger news than "merely" a 110K Tc superconductor!
Groups that typically do resistivity measurements on regularly measure low-temperature resistivities on conducting materials of ~ 10s of micro Ohm m. So if you're measuring in this range on a conducting material and hitting the noise floor with a SHARP drop, that's a pretty big indicator of superconductivity (assuming you haven't just broken your contacts which is a concern when cooling things down). I'm not so familiar with PPMS systems, but I imagine it has some built in auto-adjust on the sensitivities to where you can be pretty confident your noise floor is below these values.
What is complicating the interpretation here is the log scale (and lack of conversion to resistivity): It is amplifying the impression of the noise below what they call Tc, and making it harder to interpret the approach of the material to the transition point. The behaviour at the approach to Tc also doesn't really look like a metal, which should scale as propto T, or a semiconductor which should increase with decreasing temperature. Possibly a result of it being some horrible mixed phase ceramic.
But looking at that graph, it would be an incredible coincidence if the resistance dropped like it does and then suddenly stabilized to some very small but nonzero value… That would probably require entirely new physics to explain and would be a much bigger news than "merely" a 110K Tc superconductor!