Is it true that in US law jurors are not actually judging guilt, but rather whether the case against a person has been made in accordance with the concepts of all reasonable doubt? This meaning that US laws allows the possibility for an innocent person with an inept defense to be found guilty and also a guilty person faced with an inept prosecution being found innocent.
Is this concept discussed somewhere in the US Constitution maybe?
Short answer, yes, jurors will typically render a decision of guilt vs. innocence. This is pretty common in nations where the legal system is derived from British Common Law (about 2 billion people world wide live in a Common Law nation). The U.S. is unique in that it uses juries for Civil Trials as well as Criminal Trials. The right to a trial by jury is guaranteed in the U.S. Constitution in which the 6th amendment guarantees the right to trial by impartial jury (contrary to popular opinion, it is not a jury of peers, as this alludes to the Peerage systems, which the U.S. never adopted). That line is from the Magna Carta which was influential in the drafting of the U.S. Constitution and Bill of Rights.
A jury usually consists of a panel of 12 people pulled from the locality of the crime, unless a change of venue has been granted because the alleged crime is so well known an impartial jury cannot be seated from the population. The jury will hear all the evidence from both sides, as well as opening and closing arguments. They will be provided "jury instructions" by the judge and must find if the evidence presented (The Facts) meet the criteria for a conviction of a charged crime (The Law).
In all Jury Trials, a Jury fills the role of "Trier of Fact" while the Judge fills the role of "Trier of Law." While the judge has the education background to understand what the law says constitutes a crime and how to find that law as well as how to make sure the defense and plaintiff/prosecution make fair arguments, any random group of 12 people can understand facts and put together whose story they believe, the defense's or the prosecution's.
In the case of an innocent person being convicted due to inept defense, this does happen and is horrible, but there are recourses in the form of appeals courts, which can overturn a trial and order that a new one be held (a mistrial, essentially, the original trial never happened and the person is legally innocent. Try again and do it proper this time.) Ineffective assistance of counsel is a valid grounds for appeal of a conviction and does happen.
In the other scenario, an inept prosecution, this does happen as well and it's not the fault of the jury that the guilty person went free, but for the prosecution. The prosecutor is at a disadvantage in every criminal case to balance out the fact that their office has more resources to bring to bear then most defendants. Among these handicaps is that their "story" about what happened must not have any "plot holes" in it (beyond a reasonable doubt evidentiary standard of proof) and that the prosecution has to convince 12 people that their story is the only way this could happen (try convincing 12 random people to agree to anything more complicated than "the sky is blue and grass is green") and they only have one shot to do it (Double Jeopardy essentially bars the prosecutor's office from initiating the appeals process... and blocks someone who is declared innocent from doing it because why the hell would you want to?!). Here, the problem is that the Prosecutor doesn't have to charge the accused right away and has a bit of generous time to investigate (depends on statute of limitations on particular crimes) ... but the right to a speedy trial means that once charges are filed, the clock starts on how long the prosecution has to bring the case. Delay to long and the judge will give a directed verdict that the person is innocent because the prosecution wasn't ready.
The importance of this fact that is a staple belief of Common Law is in the "Blackstone Ratio" which states:
Better that 10 guilty people go free than a single innocent person suffers
So the jury finding the prosecution inept is certainly the prosecutor's problem, not the jury's problem. It's a feature not a bug. If an innocent person does suffer, then we have a bug and we must see that it is corrected.
As a final note, the jury also has the power of Jury Nullification of the Law. In the U.S. it's not really certain if Jury Nullification invalidates the law completely but in effect, it allows the Jury to declare a person innocent because, while they believe the prosecution's story that the defendant did what they were accused of, they don't believe this person should be convicted because they believe the crime they're accused of should have never been a crime in the first place.
Is it true that in US law jurors are not actually judging guilt, but rather whether the case against a person has been made in accordance with the concepts of all reasonable doubt?
It is not true, legally speaking, because as far as the law is concerned it is the jury's verdict that decides the question of guilt, and the jury's verdict is determined by judging whether the case has been proven beyond a reasonable doubt. The jury therefore does judge guilt when it judges whether the prosecution has met its burden of proof.
If you want to ask about "guilt" more philosophically as the determination of whether the person actually committed the crime, well, that's generally unknowable, which is why the legal system came up with the idea of "reasonable doubt" in the first place.
As others point out, there's also the question of the application of law to various factual determinations, but those questions are generally settled before (or sometimes after) the jury's deliberations, and anyway that doesn't seem to be the issue you're trying to get at.
The jury determines guilty or not guilty, which could be phrased as “prosecution has proven the case” or “prosecution has not proven the case.”
Prior to conviction they are supposed to be presumed to be innocent, after conviction they are presumed to be guilty. Ineptitude only matters on the defendant’s side, as double jeopardy prevents inept prosecutors from retrying they case until they get it right. Gross ineptitude can be grounds for an appeal on the part of the defendant, although it’s really rare for that to succeed.
In the US the Jury is considered the "Fact Finder" so they are being asked to decide which of conflicting facts is true or false. One of the facts that is being contested in a criminal case is "did he/she/they do it?" The state says yes, the suspect says no. The Jury decides which statement is true.
If a fact is uncontested then the Jury doesn't decide on it.
There are different standards of proof depending on the type of case or the court it is heard in (civil or criminal).
Also in some instances the Judge can be the fact finder, foregoing a jury all together.
