The numbers are inconsistent:

" 33 incorrect indications of negative or incorrect rejections of 30 positive sample presentations"

An "incorrect indication of negative" is exactly the same thing as an  "incorrect rejection of positive"   so if the wording was correct they both should have been the same number.   Obviously the wording was in error but it's not clear what the error was.

While 33 is close to 30, the difference is not great, but still ...     The inaccuracy makes it impossible to calculate directly the rate of false positives and rate of false negatives.

False negatives probably wouldn't be much of a problem because
1) they'd likely be due to a case where a person was not yet enough infected for metabolic changes to have occurred at a level detectable to the dogs  - so if the test was relied on for only a short time frame (3 hour flight, etc)  they've be much less likely to infect someone else than most cases
2)   even if you miss a few very early, and therefore weakly infective cases, using the dogs would obviously greatly reduce the spread of the infection, since it's all about getting the ROI (rate of infection) down and the dogs would unquestionably accomplish that.

A potential problem with false positives is what is done with them.   If they are grouped together, you'd be almost assuring that the false positives would then become true positives.

Both the 30 and 33 are false negatives (AS STATED).  It either of them was actually false positives then the false positive rate is around 20%.       So for every 4 (or so) infected individuals you isolate, you would be mixing one actually uninfected person in with them.    IF they are kept isolated from each other that's not a problem.    Because of the high rate of false positives they should be, but WILL they be?