Very much so! I have seen hardware being accepted and rejected on the basis of those limits. There were also cases where medium sized defects were reworked and rectified after careful assessments and reviews.
> With this being metal, small defects tend to grow over time- called metal fatigue
The tank and feedline welds don't cycle too often. But that also makes it very critical in reusable rockets. It may fly fine ten times and then show up unexpectedly.
> I don't know how "close to the edge" the design is
That's the fun part! As you suspect, they have ridiculously low structural margins in order to optimize for mass. What it means is that many physical phenomena that you don't usually worry too much about (when margins are splendid), suddenly turn into critical issues. Then you're off to doing doing materials research and other scientific studies, instead of doing just design and engineering (rocket engineering suddenly becomes rocket science. literally!). I've seen cases where the engineers were forced to study the algorithms used by finite element analysis software used for structural simulations. It can get that 'close to the edge'!
With this being metal, small defects tend to grow over time- called metal fatigue. This all depends on the stress in the material which depends on a lot of things: fluid flows and pressures, temperatures (and temperature differences and rates of change), vibrations (structural or induced by fluid flow), etc etc.
Mechanical engineering at this level is very complex! So many of these things boil down to probability distributions of each process involved. I don't know how "close to the edge" the design is, but this is the kind of thing you have to do when optimizing for weight.