That's about as deceitful as Ben Wallace claiming that Boris didn't actually tell him to do anything.
It doesn't need a specific instruction from one individual to another to pass an instruction, desire, or wish down the line of command.
The emails specifically say, "authorised by the PM".
We understand the current chaotic culture in No 10, but that chaotic culture does not explain, is not sufficient, and is no defence for lying, on the basis of, "I didn't know what I was doing, when I did it."
A special plane was chartered to fly out the animals. That plane could easily have transported people.
That plane took up bandwidth (flying/landing/loading/taking off/guarding/organising, etc.) which could have been used to evacuate people.
A C 17 can carry about 800 people, that one was used to carry about 180 animals.