In allowing her appeal, NSW District court judge Clive Jeffreys was not satisfied beyond reasonable doubt that Ms Matthews was the person who signed the statutory declaration making the complaint, as the person wore a full-facial veil.
The judge also was not satisfied that even if she did sign it, that she knew the declaration's contents were false.
Ms Matthews subsequently applied for her legal costs, but today Judge Jeffreys dismissed her application.
"I am not able to find that the investigation into the alleged offence was conducted in an unreasonable or inappropriate manner,'' he said.
"It is not sufficient, in my view, to say that other people could have been spoken to, or that advice could have been obtained.
"The reality is, when one looks at the material, it was open to a tribunal of fact to be satisfied beyond a reasonable doubt.''
He noted "different minds'' might have made different findings, but he had not been satisfied beyond a reasonable doubt.
Judge Jeffreys said he also could not find that the proceedings were initiated without reasonable cause.
He said the material available had included the statutory declaration.
"On one view'', the signature could be said to be similar to the one on Ms Matthews' driving licence, he said.
"There is no suggestion in this case, and certainly no evidence to the effect, that the proceedings were initiated in bad faith,'' the judge added.
Outside the court, Ms Matthews' lawyer, Stephen Hopper, said he could not give an estimate of his client's legal bill but said she would accept the judge's decision.
"She is happy she did not have to go to jail and her name was cleared,'' he said.
The case prompted changes to the law last year to enable police to require anyone to remove a face covering, including a helmet, burqa, niqab or mask, for identification purposes.
If they do not comply, they face fines or up to a year in jail.
- AAP
