A segment on August 10 saw reporter Simon Jones broadcast live from alongside a dinghy containing some people who said they were from Syria. Cameras caught their packed inflatable getting into difficulty.
After providing commentary on the "pretty dangerous" situation the people were in, he waited until the occupants were picked up by the UK Border Force.
Some 8,340 complaints were made on the grounds that viewers felt the programme showed “offensive/insensitive coverage of migrants".
During the segment, Mr Jones said: “We have seen them trying to get water out of the boat, they’re doing that at the moment, they are using a plastic container to try to bail out the boat.
“Obviously it’s pretty overloaded there. People are wearing life jackets, it is pretty dangerous, just the number of people on board that boat.”
After asking whether they were safe, Mr Jones remained with the boat until help came.
A BBC spokeswoman said: “This report was a stark illustration of the significant risks some people are prepared to take to reach the UK.
"Channel crossings is a topic of huge importance and we always endeavour to cover the story sensitively. In this instance, the Dover Coastguard were aware of the boat before our crew spoke to them and at no point did they, or those in the boat signal that a rescue operation was required. The Coastguards instead alerted Border Force, who then safely picked up the occupants and took them to shore.”
The BBC report also detailed other complaints made to the company and noted that in some instances invitations to complain had been posted online.
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Another 508 complaints were made to the BBC over a news report which contained a racist term, additional to the 18,656 who initially objected.
During a report last month on a suspected racially-motivated attack in Bristol, social affairs correspondent Fiona Lamdin repeated a racial slur which was allegedly used during the incident.
The story ran on the BBC News Channel and local news programme Points West on July 29, although later that day the broadcaster stopped running the report which featured the offensive language.
The corporation initially received a total of 18,656 complaints up to August 2.
Between August 3 and 16 it received an additional 508.
BBC Two documentary American History’s Biggest Fibs, hosted by Lucy Worsley, also drew 158 complaints after using the racial slur.
It came during a repeat which aired on August 1, tackling the subject of the US confederacy and the freedom of slaves.
Ms Worsley later apologised on Twitter, saying her use of the word “wasn’t acceptable and I apologise”.