Does a US immigration officer really have the power to deny entry to the country at personal will?

Yes, they have the power, but:

• it is all recorded, and somewhat appealable (you may not get in this time, but next time)
• an agent showing a pattern such as always denying fat people, or people of a certain religion, would risk discipline, there is supervision and management
• most of them are good decent people who believe they are protecting their country, and not just from "terror" or "job stealing" but from things like food diseases and pests.

All these jobs have qualifications to get them, and oversight. If you watch Border Security etc you will see agents going to their supervisors and laying out what they've found, for example. It is true that an agent having a bad day may feel that you're lying, and refuse you even if you're not. It's not true that this makes entering a country into a lottery.

The power to deny entry lies with just about every immigration official in every country, it is not unique to the USA. Even with proper visas, the immigration official has the final say to allow or to deny your entry.

As others have pointed out, there are procedures to be followed before a denied entry occurs and most of the time there are avenues of recourse (such as having a supervisor included in the conversation or requesting a redress before your next trip).

I would hazard a guess that the number of people denied entry because the immigration officer was having a bad day or some other such nonsensical reason would be miniscule. Most denied entries are based on a solid reason, inability to show financial support, improper documents, old offenses still lurking in the databases, aggressive attitude towards in immigration officer's questions, etc.

If you meet the requirements for entry, then you really have nothing to worry about. If you are entering with borderline qualifications, then it can be a bit of a lottery. If you are entering with improper documents, then it is a brick wall.

Regardless of the rules, from personal experience I can say that in practice one individual officer can indeed arbitrarily block your entry when they are having a bad day.

A german friend of mine was accepted at a US university, and went to the Embassy in The Hague (Netherlands).

She had prepared all documents to apply for the visa and after having them reviewed, the officer (a woman who seemed to dominate the department) simply said No.

Upon asking what the problem was, perhaps whether any documents were missing she simply answered:

I Just don't believe that you are going there to study

After this arguments did not help and my friend was left speechless.

She contacted the university, got a letter of recommendation from them and they helped her get a new appointment.

This time procedures made sure that her case was not handled by the same person. The officer helping her was less intimidating.

Whilst reviewing the documentation all seemed well, until the dominant woman appeared again, gave her a quick look and simply said No.

After this the guy handling the case looked very embarrassed, stopped examining the documents and rejected my friend. After the dominating woman left he whispered:

I'm sorry but you shouldn't apply here again. Perhaps your school can make the visa for you

So, to conclude: Even if you have all proper documentation, you can still get rejected without (what I would consider) a proper reason. I won't go into detail on how this impacted my friend but always make sure you have a plan B in place, and think twice before betting on being allowed into the US.

This policy does exist, as has been previously mentioned. It is important to understand that the reason this policy exists is to delegate the appropriate authority to act to the individuals who have the sworn duty to protect the country's borders. The policy is intended to give authority to the officers on the "front lines" of the border, interacting with the travelers. It allows for situations where things just don't "feel right".

Consider the case from the incidents of September 11, 2001:

[US Customs and Border Patrol Officer] Jose Melendez-Perez received applause from the commissioners and spectators as he described how on Aug. 4, 2001, he refused to allow Mohamed al-Qahtani, whom some commission members described as the probable 20th Sept. 11 hijacker, to enter through the Orlando airport based almost entirely on a gut feeling the man was lying.

"I felt a bone-chilling, cold effect," he said. "He gave me the chills."

Credit: Baltimore Sun, Sept. 11 hijacker raised suspicions at border

As has been mentioned, for better or worse this is completely normal;

that is to say, every country operates in this way at the border.

(Indeed an interesting question is ... is there any country which is an exception to this? i.e., is there a country you are "absolutely" allowed to enter, and the border officials literally cannot stop you (!) ... Is there such a country?!)

Regarding the USA case, I'm afraid I couldn't find the actual document explaining that an immigration border officer has this power. (Again it's hard to see how "they couldn't," but I couldn't find the relevant law or document.) Here however is the relevant assertion for one particular visa type:

https://travel.state.gov/content/visas/en/visit/visa-waiver-program.html

"An approved ESTA (Electronic System for Travel Authorization) allows a citizen of a Visa Waiver Program participating country to travel to a U.S. port-of-entry (generally an airport) and request permission to enter the United States. An approved ESTA does not guarantee entry into the United States."

(emphases added)