Let's take the example of chemical contamination in a reservoir. If chemical x is present at a concentration that is at or above the Reporting Level for that particular chemical using a specified analytical method, the chemical can be measured, both in terms of its identity and within the prescribed statistical requirements (i.e., accuracy, as dictated by precision and bias) of the analytical method.
If the same contaminant is present at a concentration that is below the Reporting Level but above the Detection Limit for the chemical/method, the contaminant can be identified, but its concentration cannot be measured with reliability that is sufficient to meet the statistical requirements of the method.
If the contaminant is present at a concentration that is less than its Detection Limit, it can neither be identified nor quantified because its signal cannot be sufficiently differentiated from that of the instrument signal derived from a blank.
Now you might counter that if it cannot be measured, then how can you know it's actually there to be measured? That is a philosophical question rather than a scientific one. My point is that it is possible for a contaminant to exist in a water body at a concentration that is not capable of being measured because the ambient "noise" in the system is greater than the signal caused by the contaminant.
If we improve the technology to the point where the ambient "noise" of the system is reduced, the concentration down to which we can measure gets lower, yes, but there will always be some finite concentration that is theoretically less than the lowest concentration that an analytical method/instrumentation setup can measure. This is because there is no such thing as zero in the field of analytical chemistry, just "less than I can detect," or "less than I can reliably measure."
Further, as one reduces the inherent noise in the analytical setup, the likelihood of cross-contamination from human breath or other diffusive processes from the body can start to play a larger role. You then become uncertain as to whether chemical x was truly in the water sample or if it came from the analyst (this is a real problem in these days of ng/L analytical technology). If you have that level of uncertainty in a result, even if you get a result, one could argue that one hasn't really measured anything.