Others have already addressed this, but no, as many of us have already said, it is not required and that is not a good source of information. Generally speaking, if someone is trying to sell you something, it's best to double-check their information with an independent source.
If you want to do the tasks you mentioned (medicating, etc.) why not become a veterinary technician? The pay is still low, but it is significantly higher than a veterinary assistant's salary and you'd get to do more. Paying for a certificate to be a vet assistant does not make sense, but becoming a registered veterinary technician (RVT) and getting the education necessary to do so could be a good choice for you.