What is the record for greatest number of athletes with the same finish time in one event?

I looked for recorded instances of the same finishing time by more than 3 runners, and couldn't find any. As was mentioned in the comments, the race you referenced in your question was reported to 0.01 seconds. A quick online search showed that they eventually ruled based on the photo finish camera (those results can be seen in the photo you included in the question).

Based on my research, I'm fairly certain that at the 0.01 seconds scale, the instance you pointed to, 3 runners, is the most ever recorded. Another instance of this was in 2015, at the IAAF World Championships in Beijing. In the men's 100m, 3 runners, Tyson Gay (U.S), Asafa Powell (JAM), and Jimmy Vicaut (FRA) clocked in at 10.00 seconds (correct to 0.01s). Again, these runners were eventually ranked in fifth, sixth and seventh place respectively, based on the footage. Interestingly, at that same race Trayvon Bromell (USA) and Andre De Grasse (Canada) both came in at 9.92s. In this case, their results were declared a "dead heat", in which a judgement cannot be made, and a tie is declared. Both were awarded the bronze medal.

If we're looking for, as you originally wrote, "athletes finishing with the same time", and we're really after a dead heat that's declared as such, it seems that 2 runners is the most ever recorded. Other than Bromell and De Grasse, the most well-known case of this is the Tarmoh/Felix third place tie at the USA Olympic trials women's 100m in 2012. I know you asked for international competitions, and this isn't one, but I just think it's a great example of what happens in such an event. Since they could not be declared tied (only one of them could qualify and move on to compete in the Olympic games), they were given a choice between a coin-toss and a runoff. They both agreed to a runoff, but Tarmoh ultimately decided to withdraw from the runoff, feeling that she'd been wronged by the organization, and thus gave up the spot to Felix.

If you want to read more about these cases, and more broadly about the ties in sporting events and the discipline of timing and imaging (and its limitations), I highly recommend reading Jonathan Finn's article on the subject.