You are wrong, and here's why.
With no measurements at all, you cannot make informed judgments about the quality of your software. You can only guess. This means you would be unable to convince anyone (sane and intelligent) that your product has n bugs. "Because I say so" is not a metric.
With a poor measurement--such as one that ranks all defects equally--you have information, but now it's bad information. If you share the information but not the method(s) used to gather it, you can convince people you're right, because you have data about it. Never mind if you are stacking up Product A with 1 show-stopping bug against Product B with 50 cosmetic bugs or unhandled corner cases. By this bugcount-only metric, Product A looks better, and that's just stupid.
You need good measurements, and sometimes that includes measurements which cannot be quantitatively calculated without human intervention. A human programmer (or QA or other support person) who is familiar with a product will know just how severe a given bug is in terms of its impact. It is why, after all, bug tracking systems generally allow you to prioritize work by severity, fixing the worst bugs first.
Poor information is worse than no information because it can lead you to make the wrong decisions with confidence. With no information, at least you know you are shooting in the dark.