In a Facebook post Ms Chintamunnee claimed the staffy mauled one of the dachshunds, Coco, to death and that the owner just walked away after the attack.
But Ms Harrison defended her actions, claiming she was walking her dog on a lead with her son when the three dogs ran over and started attacking Hero.
She said she was trying to protect her son while separating the dogs, but by the time Coco's owners came over it was too late.
A Change.org petition has since been set up to save Hero from being put down following the incident.
The woman who started the petition, Emma McLean, claimed the staffy may be put to sleep "because of the negligence of Coco's owners".
"Hero's owner was doing the right thing, walking her dog on a leash in a leash only area," Ms McLean wrote.
"Coco, a dog half the size of Hero (as well as two other dogs) attacked Hero. Coco was a small breed and it is inevitable that in an attack a larger dog would cause extensive damage to a small dog."
She described Ms Chintamunnee's version of events as a "fake story", which resulted in her "vilifying Hero and his owner".
"Thankfully the true story as well as CCTV footage has emerged showing what really happened," Ms McLean wrote.
"Coco's owner has changed her story so many times now to try to look innocent and vilify Hero, and that speaks volumes.
Ms Chintamunnee was left covered in blood. Photo / Facebook
"RIP Coco and condolences to her family, but lying to sentence another dog to death is just disgusting."
Ms McLean said the aim of the petition was to urge Cardinia Shire Council not to put Hero down.
"Lets not make an already heartbreaking tragedy worse by putting a dog to death for defending himself and his family," she wrote.
More than 10,000 people have signed the petition calling for Hero to be saved.
The incident gained national attention after Ms Chintamunnee posted about it on Facebook, uploading photos of both Hero and herself covered in Coco's blood.
She previously told the Cranbourne Leader her father opened their gate and Coco, aged four, ran outside.
Ms Chintamunnee said the staffy started Mauling Coco after the smaller dog "sniffed" him.
"The dog had bitten too deep into Coco's main vessel as he had lost that much blood – I was drenched in his blood that's how much there was."
Mrs Chintamunnee rushed to two nearby vets that were closed and Coco died a few minutes before she arrived at the third.
But this version of events was later contested by Ms Harrison in a statement read out by her husband Paki.
She said in the statement that the three unleashed dogs approached her and her son from behind as they were walking Hero.
"The larger dog started to bark aggressively and I tried to get my son behind me to keep him safe and pull my dog away at the same time," Ms Harrison said.
More than ten thousand people have signed the petition to save Hero. Photo / Change.org
"My dog was on his lead with a harness. I looked around but there was no owner in sight and I was worried for my son."
She said she couldn't get the dogs away and keep her son safe at the same time so she waved down some other people who happened to be the owners.
Mrs Harrison said Mrs Chintamunnee's husband told her he let the dogs out of the garage.
She said the family had informed the owner of the dachshund their details but they had "not bothered" to contact them.
