The Venue 
The Elbphilharmonie (also English: Elbe Philharmonic Hall) is a concert hall in the HafenCity quarter of Hamburg, Germany, on the Grasbrook (de) peninsula of the Elbe River. It is one of the largest and most acoustically advanced concert halls in the world.
The Elbphilharmonie has three concert venues. The Great Concert Hall can accommodate 2,100 visitors whereby the performers are in the center of the hall surrounded by the audience in the vineyard style arrangement. The acoustics were designed by Yasuhisa Toyota who installed about 10,000 individually microshaped drywall plates to disperse sound waves. The Great Concert Hall contains a pipe organ with 69 registers built by Klais Orgelbau. The Recital Hall is intended for the performance of recitals, chamber music and jazz concerts; it can hold an audience of 550 people. In addition, there is the Kaistudio that allows for 170 visitors and is intended to serve educational activities. Likely the site of the dinner, which followed the concert, likely held in the Recital Hall.
The G20 Heads-of-State, their spouse, one translator each and the wait staff.
Heads-of-State and their spouses were separated, Melania Trump was seated to the left of Vladimir Putin and right of Argentine President Mauricio Macri. While Donald was seated, on the opposite side of the table, to the left of Akie Abe, wife of Japanese Prime Minister Shinzō Abe.
Translators had chairs arranged along the walls behind their principles. When needed they would move into position between their principle and their conversation companion. It is widely reported that Putin and Melania didn’t need a translator because they shared a common language, German. This photo tends to disprove that assertions, it appears that the translator is an active participant in the pre-dinner conversation between Melania and Putin. Putin’s translator would have been Russian/English as he was seated next to Melania.
POTUS, lower left, was seated between the wife of Argentinian President Juliana Awada on his left and Akie Abe, wife of Japanese Prime Minister Shinzō Abe on his right. His translator, who spoke Japanese, is seated directly behind him.
The dinner took place after the concert, which began at 8:00 PM, one report has the dinner still underway at 10:40 PM.
Ian Bremmer, president of the political risk consultancy firm, Eurasia Group, reportedly broke the story of the meeting, even though he was not present, his source has not been reported. In a note to his clients, Bremmer reportedly wrote:
Halfway in [the dinner], Trump gets up from his seat, sits next to Putin, and spends roughly an hour talking privately and animatedly with the Russian president, joined only by Putin’s own translator. … Several notable pieces here. One, that Trump didn’t bring in his own translator — a breach of national security protocol Trump likely wouldn’t be aware of, but that significantly advantages the meeting towards Putin.
I find this scenario difficult to believe; getting up in the middle of a State Dinner and either having Melania or the individual on Putin’s right move, which wasn’t reported. Tthis would have been noticed by others at the meeting, unless it was at the end of the meal when people were moving around being social.
The image of Putin, Trump and Putin’s translator huddle at the table, out-of-earshot of others (reported elsewhere), half way through a State Dinner is hard to conjure. It should be easy to verify, I am sure an enterprising reporter could find someone on the wait staff to confirm the story, as it would have disrupted the flow of serving the remainder of the meal. Likewise the Senate can call the translator, presumably a government employee, for verification. A simple yes/no question; “Did POTUS get up from his place at the table and sit with Putin, for an hour, midway through the meal?, without all of the normal grandstanding that goes on in the Senate hearing.
The White House version:
The White House confirmed that Trump and Putin spoke at a dinner for G-20 leaders and their spouses. But a White House official appeared to dispute that the discussion lasted an hour, saying the two only spoke “briefly” near the end of the dinner.
We have a difference of when, midway vs near the end and length, hour vs briefly. I can envision a meeting after desert, as the dinner is breaking up, when POTUS had come over to talk with FLOTUS. But, at that point, in the evening, an hour meeting is very implausible.
Myth 1 – “Only the Russians will have a transcript” 
There is no transcript, the meeting was NOT recorded, Putin and his translator could have contemporary notes or recorded debriefing, written or recorded after the meeting. I would hope (expect) that POTUS has the same.
Myth 2 – “Secret Meeting”
It is hard to hold a secret meeting in a room with 80 – 100 witnesses. Undisclosed, or unreported OK, but secret, not hardly. Vanity Fair reported it as a “private encounter”, private is hard to come by in a room with 80 – 100 people. Likewise his conversation with others at the dinner have not been “disclosed” nor reported.
Myth 3 – “Strange … no national security official was present”
Given that the only three US representatives were POTUS, FLOTUS and a (State Department ?) translator it would have been impossible for a national security team member to be there. Again, there is no reportage nor scandal or national security concerns relative to any other “encounters” POTUS had at the dinner.