Is it possible to be denied entry into USA after being granted a tourist visa by my local embassy?

It is clearly mentioned in a few answers here that a pre-issued visa is not an entry permission but a permission to travel to a port of entry and request that permission. So the person at immigration will not ‘override the embassy’s decision’ but rather ‘come to a different conclusion in their own decision’. For example, on the United States CBP website it says

Issuance of a visa does not guarantee entry to the United States. A visa simply indicates that a U.S. consular officer at an American embassy or consulate has reviewed the application and that officer has determined that the individual is eligible to enter the country for a specific purpose. The CBP Officer at the port-of-entry will conduct an inspection to determine if the individual is eligible for admission under U.S. immigration law. (source)

In most if not all countries, the decision of whether to let somebody enter the country or not is down to the immigration officer inspecting your documents at the immigration check (and maybe that officer’s supervisor). This means that you can still be refused if:

• people from your country generally don’t need visas
• there is a visa waiver agreement or similar for certain conditions requiring nationals of your country to submit certain information but not actually issuing a visa and you are eligible
• nationals of your country typically obtain visas on arrival and there is nothing prohibiting you from getting one
• you applied for and got granted a visa which is valid during your intended travel dates

One example for the last bullet point (unfortunately from the Schengen zone, not the US) is ‘Denied entry into Schengen zone: Can I still use my visa?’ Therein, OP was denied entry to Germany because they could not satisfy the immigration officers that they wanted to leave (in a nutshell: OP had a flight from Germany home but no flight from Portugal to Germany).

Now of course, if you submitted all your documents in a timely manner and the embassy does decide to grant you a visa, then probabilities have suddenly drastically changed. In the overwhelming majority of cases, those applying for entry with a valid visa are let in — because the difficult cases are usually identified and weeded out at the visa application stage by rejecting them.

In your case, you mention that a previous trip to Iran is the basis of your uncertainty. The US embassy will have ample time to investigate your backgrounds and the details of that trip based on the documents you provide. If they come to the conclusion that you are admissable despite the Iran trip, that is very strong grounds for the immigration officer to consider that part handled and not make it affect his position.

It still bears repeating though, that it is all and entirely up to the immigration officer on duty and their superiors whether you are let in or not.

It's always possible, but not likely.

I've been denied at a border for which I had a valid visa. It wasn't even anything personal, just that there were elections upcoming and they decided to close the border.

Fortunately, the country we had just left was reasonable, when we turned around they basically cancelled our leaving, thus allowing us back in despite not having valid visas. (We all had single entry visas which had already been used.)

The immigration officer would need a reason that would make you inadmissible to deny you entry. A visit to Iran in itself is not a valid reason to deny entry. My friends who have visited Iraq many times have never had a problem going to the USA. Occasionally, they're questioned about their visits there, but "just visiting x y Z" is a good enough answer.

The immigration officers and their superiors will not deny you entry just because you visited Iran. They are not allowed to do that. If they do, you may request for redress. (https://help.cbp.gov/app/answers/detail/a_id/757/~/friend%2C-relative%2C-etc.-denied-entry-to-the-u.s.) The reason for your denial would be logged in the CBP system and would be considered during the redress process. It would be unlawful for an officer to deny entry for a reason that does not make the traveler inadmissible. A visit to Iran or Iraq does not make a traveler inadmissible.

You are concerned they may deny you entry on "security grounds." Visits to Iran do not make you a security threat.

While the final decision to let you in rests with the officers, it does not mean they are above the law. They have rules that they must follow and if violate any law they will be answerable.

Before starting to worry about being refused entry at the US border you should examine the relevant statistics from CBP:

On a typical day, CBP:

• Processed 1,069,266 passengers and pedestrians

• Refused 350 inadmissible persons at U.S. ports of entry

So your chances of being refused despite having a valid visa are 0.032%. Personally I find these odds good enough to completely avoid worrying about a possible denial of entry.