I would imagine so but it just seems a bit over the top. They don't say "intentionally false", they just say "false". If someone makes a mistake, they have falsely ellicited help from Pogo and may suffer bad consequences. I know someone who claimed to be missing a SOL GAR badge that is listed early in the list. She got the badges after the one in question. She contacted Pogo and didn't get much satisfaction. When she reached the end of the garden, the badge was there. Maybe Pogo listed the badges out of order, I don't know. That would have been a false claim but an innocent one. Threatening her with possible banning seems harsh and out of proportion.
Having said all this, I wouldn't want to be a customer service rep for all the tea in China. We, the public, are a rough crowd.