The assertion wasplausible based on the video of the scene, and prosecutors failed to prove the case beyond a reasonable doubt.
The judge said that people were streaming by and the officers made no attempt to stop them.
The prosecutors argued that broken windows and loud alarms should have told Martin that he did not have permission to enter, but the police conduct undermined that evidence.
The ruling is a blow to the Justice Department and is likely to elevate similar defenses from hundreds of other members of the mob who have claimed that they didn't know they weren't permitted inside the Capitol.
Martin testified in his own defense and said he believed he was waved into the lobby by an officer.
The way the officer briefly interrupted the flow of people and then stepped back to allow it to resume could have given Martin that impression.
The judge said that the defendants reasonably believed they were allowed into the Capitol.
He said that the officers were grossly outnumbered at that point.
The judge said they acted reasonably.
The verdict could be seen as a message to prosecutors that pursuing criminal charges against nearly every demonstrator who entered the Capitol on January 6 was foolish and that resources should have been trained more intensely on those accused of violence or of conspiring to block the electoral vote count.
Martin's conduct was about as minimal as I can imagine, among the Jan. 6 defendants.
Martin was charged with entering and remaining in a restricted area for a Secret Service protectee, disorderly conduct in such an area, and parading or demonstrating in the Capitol.
The judge said that after Martin entered, he stayed away from the areas in the Rotunda where demonstrators were taunting and fighting with police.
He was quiet and orderly. He didn't raise his flag.
The judge said that while Martin was in the Capitol, he spent most of his time making videos with his phone, which was not different than what members of the press were doing.
The judge said that the first charge against Martin was a close call.
He told reporters outside the courthouse that he hoped to get his job back as an engineer for a government contractor in Los Alamos. Martin lost his security clearance from the Energy Department.
On Tuesday, Martin said he had an idyllic experience at Trump's rally and march to the Capitol.
He said it was a wonderful day.
The judge was urged to treat Martin's testimony with extreme skepticism, because he was evasive on the stand and had carefully crafted his answers to downplay his culpability. Martin and his attorney attended a recent trial where the judge studied how to craft a defense that might play to his previous rulings.
The rulings from the Trump-appointed judge that have disappointed prosecutors and broken sharply from colleagues on the District Court in Washington have been the latest.
The Justice Department said the defendants deserved jail time. He questioned the merit of some of the cases that the department brought against people who were not involved in the Jan. 6 mob.
The ruling shows that the rioters believed they had permission to enter the Capitol because of the actions of the Capitol Police. The police department made decisions early in the day to focus on protecting lawmakers and securing the complex rather than arresting rioters, which resulted in the nationwide search for hundreds of defendants that continues to this day.
The Capitol Police wouldn't comment on the decision.
As a matter of policy, we can't comment on any of these cases until they're done.
Nearly all of the complaints against Capitol Police officers who were active during the Capitol breach were found to lack merit. A retired officer has been charged with trying to help an alleged rioter by encouraging him to take down incriminating Facebook posts. The officer is going to go to trial later this year.
A number of people charged in connection with the January riot have pleaded guilty. There have been many different sentences, ranging from one to more than five years in prison.
Only two of the six Jan. 6 cases had been completed before Wednesday's not-guilty verdicts for Martin. Guy Reffitt, a Texas militia member, was the first person to go to trial on January 6.
A bench trial was held for the second case, that of the New Mexico county commissioner and Cowboys for Trump founder. There were two counts of entering a restricted area. He was acquitted of disorderly conduct, but found guilty of being on the premises.
Both men will be sentenced.