Experienced chopper pilot Armstrong, 63, despite being grounded after suffering a mini-stroke, answered a plea to help and rescued Mr Lee from his "precarious" position.
Rescuers, and Mr Lee, fear he would've died if Armstrong had not stepped in.
However, the Civil Aviation Authority (CAA) charged Armstrong with breaches of the Civil Aviation Act.
Judge Tony Couch today rejected an application for a discharge without conviction.
Armstrong earlier admitted that on April 5 last year he flew a Robinson R44 helicopter without an appropriate medical certificate issued under the Civil Aviation Act and that he failed to accurately record flight details in his pilot logbook.
He also admitted flying without a medical certificate on April 21 last year during a police search in the Clarence River area.
Related charges against Kaikoura Helicopters Limited were dropped.
This morning at Christchurch District Court, defence counsel Craig Ruane said Mr Lee had been in a "life and death situation".
To expect Mr Armstrong to say, "I'm not going to do this", and let Mr Lee die, was not a realistic option, Mr Ruane said.
A conviction would send a "dangerous signal" to all pilots, especially those involved in search and rescue, and would "inevitably lead to loss of lives", he said.
CAA lawyer Chris Macklin said the case was a "very simple" and "very serious".
Mr Armstrong has demonstrated a sustained contempt for aviation laws, he said.
A discharge without conviction would send a "very unhelpful message" to the industry, Mr Macklin added.
Earlier Armstrong feared what message his case could create.
He said: "We'll end up being a nation who don't care a rat's about anybody. That's why it's probably got so much public support."
An online change.org petition backing Armstrong's actions has received more than 5000 supporters.
The rescued hunter, Mr Lee, who was in court today, earlier said he would've died if it wasn't for his rescuer.
"Dave truly is my hero," said Mr Lee, who broke his femur in the fall down a steep scree slope.
"I can't express how much gratitude I have towards him. Being here today meant a lot to be here with Dave."
Mr Lee was "devastated" that his rescuer was charged. He criticised the CAA's hardline stance.
"How much do [CAA] value a human life? Does it really come to the paperwork - the fact he failed that medical certificate? He'd done the tests to prove he was right."
In considering whether a discharge without conviction was appropriate, Judge Couch said he had to first assess the gravity of the offending, then the direct and indirect consequences of a conviction, and whether those consequences are out of proportion to the offending.
During the April 5 rescue, Armstrong was in control of the chopper for around 10-15 minutes.
But Judge Couch said it was a flight during difficult conditions, close to hills, and Armstrong was the only pilot.
"It was a high risk situation," the judge noted.
"Had he suffered even a momentary loss of awareness or control, there was the very real possibility of death or injury to the four people in the helicopter."
Even though the April 5 situation was an emergency, the CAA rules meant Armstrong was not allowed to fly, no matter what.
"Even in a life threatening emergency, the defendant was not permitted to operate the helicopter," Judge Couch said.
It would be "fundamentally wrong" for the courts to make a ruling against the CAA rules, he added.
The summary of facts describes the second incident where police - unaware that Armstrong had been grounded due to his medical condition - asked him to help search for three people overdue from a kayaking trip on the Clarence River on April 21 last year.
Armstrong flew a fellow pilot and a police constable in the search before being stood down as the missing trio were located elsewhere.
He later admitted asking his fellow pilot to document the entire flight - as he did with the rescued hunter - in their pilot logbook and not his own.
"The purpose of the Act is to establish rules of operation and divisions of responsibility within the New Zealand civil aviation system in order to promote aviation safety," the CAA's summary says.
"As the aviation safety regulator, the CAA has an obligation to promote aviation safety and security in the interests of the general public."
After the sentencing, Mr Lee said he was "really gutted" for Armstrong, who since the rescue, had become a close friend.
"To get a conviction, after all of this, is just devastating. I owe my life to Dave."
Rescuers lack the time to make some important judgment calls, he said.
Armstrong made a snap decision to try and save a life, Mr Lee said.
"There's got to be some new rules. It's got to be more defined on what people can do in life and death situations," he said.
Outside court today, Armstrong said he was "disappointed" by the conviction.
Asked if he would do the same again, he hesitated.
"I'd have to seriously think about that," he said.
It was an "easy" decision on the day because of the circumstances."You had to be there," Armstrong said.
"Anyone had a loved one in the same situation [would] do exactly the same."
Safety was paramount, "whether the CAA realise it or not", he said.
"We all got home safe and no one is dead on the hill. That's all there is about it really."
Armstrong hoped a "Good Samaritan" rule would be introduced in New Zealand to prevent similar situations.
"Whether you're an aviator or in any voluntary situation you get yourself into, you're never immune from what happened today," he said.
"So the sooner the Good Samaritan rule comes in, the country will be better off, and people can step up, not step back."
He said he was also thankful the "overwhelming" support he has received since he was charged.
