Last 3 seconds:
As there are differing opinions about whether a time-out was given, I'm going to prove that it was not given.
First, read the article 41: Charged Time-out:
A Coach has the right to request a charged time-out.
Electrical devices enabling Coaches to request a time-out without leaving their places may be used.
The Scorer shall indicate to the officials that a request for charged time-out has been made by sounding his signal as soon as the ball is dead and the game watch is stopped but before the ball is again in play ...
Now let's watch the main video:
First, pay attention to Righetto. That's the referee who appeared in the center of the screen when the game was interrupted. That happened at second 18. At second 27, a time–out obviously had not started yet – both Soviet coaches were still arguing. At second 35, we see Righetto waving his hand, ordering everyone from the American bench to take their seats. At second 45, he decided that he had succeeded in doing that, so he started moving towards the center line. At second 47.5, Bashkin appeared in the left edge of the screen, talking to Jones. At second 48.8, Bashkin was asking Jones for a time-out. So, it still had not been given! At second 55.5, the Soviets were starting to gather around Kondrashin – it looks like a time-out. At second 57.5, the American players started moving towards their bench – it definitely looks like a time-out. But at 1.02.5, we see that Righetto tried to get Iba (the American coach, in a case someone doesn't know) back to the bench. A five-second time-out? That would be too short.
So, we can see from video that there was no time for a full 30-second time-out.
Another argument against a time-out can be made. Normally, a horn sounds when the time-out is over, but that didn't happen.
Next argument - look at the scoreboard, where all time-outs are registered.
Here is the scoreboard when there were 55 seconds left in the game.
Just above the scores there are lights indicating number of time-outs taken - 1 by Soviet and 2 by US.
Here is the scoreboard's final view.
Same thing - Soviets have one time-out taken so far.
Then, the american protest (you can find it in the Postface page) says that "The official score sheet does not show a timeout in the last three seconds.".
Also, several days after the game FIBA released "Chronological order of events", that states that "The charged time-out was of course not granted" (bullet "b").
Yet another argument is that, according to the rules (Rule 45), after a time-out the game restarts from the sideline, not the baseline. But in the game Soviets threw the ball in from the baseline.
The final argument involves the game report filed by Brasilian referee Renato Righetto. Here you can find parts of his report, in which he states that a time-out was not given.
If someone is still not convinced, they can take a look at the video of the time-out called by Iba with 55 seconds remaining.
The horn sounded at second 4, notifying everyone that a time-out had been taken by the Americans. Then another one sounded at second 9, this time notifying referees about a substitution. Players started moving lazily towards their benches. Americans are gathered at about second 20. Russians did the same at about second 30. Sometime in between (at second 28), the timekeeper started a time-out clock. The time-out ended at second 58. That's when the horn sounded again, to signify the time-out is over. Players didn't rush back, continuing to talk with the coach. Only at 1.12 did they, again lazily, return to the court. That's what a time-out looks like. That’s completely different from the events a minute later.