Hundreds of people wait for swine flu vaccination shots Monday in the City of Industry, Calif. Before Los Angeles County health officials stepped up screening at their flu clinics some people who aren’t at high risk for swine flu complications got the much-in-demand vaccine.

Los Angeles ? It was bound to happen: Some people who aren’t at high risk for swine flu complications got the much-in-demand vaccine.

Sometimes they were healthy adults or senior citizens instead of kids, pregnant women and people with health problems.

Before Los Angeles County health officials stepped up screening at their flu clinics, Natalie Thompson sailed through the long line and got the vaccine along with her 8-year-old son, even though she’s not in one of the priority groups.

“If I can get it, I’m not gonna say no,” said Thompson, 35, of Hollywood Hills.

Another mom, Katy Radparvar, didn’t say no either.

“Our doctor doesn’t have it yet,” said the 41-year-old woman who was vaccinated along with her three children at a public health vaccination site in suburban Encino last week.

Public health officials don’t want to be vaccine police. Many don’t turn anyone away who wants the vaccine, though some locations are tougher than others.

“For many this is a frustrating process and we really sympathize with those who show up at a clinic and can’t get vaccinated,” said Los Angeles County public health director Dr. Jonathan Fielding.

Across the country, thousands have waited in line and many have been turned away, as manufacturers have trickled out the slow-to-produce vaccine. Things are improving, and now about 25 million doses are available, the government says.

Aware of scant supplies up front, Santa Barbara County clinics administered their 4,400 shots to pregnant women only. San Diego County is only immunizing those on the priority list, but is taking the word of residents.

Nevada is using the honor system with vaccinations offered on a first-come, first-served basis to those who identify themselves as at-risk for the H1N1 virus.

“We really are hoping people go on the honor system and let us immunize people in the priority groups,” Southern Nevada Health District spokeswoman Stephanie Bethel said. “I think, for the most part, it’s working.”

In Oregon, Portland metro area officials say pregnant women and children are moved to the front of the lines and inoculated before the general public.

“We assertively asked those who were not in the priority group to move to the end of the line, so when we ran out of vaccine, those people who were left were those who were not at risk,” said health officer Dr. Gary Oxman. “And people have responded well to it.”

Robert M. Pestronk, executive director of the National Association of County and City Health Officials, said local health departments are doing the best they can under challenging conditions.

“Despite those best efforts, it doesn’t surprise me that people who are not in high priority groups are appearing at clinics for vaccination,” he said. “It’s difficult to restrict vaccine simply to the priority groups.”

One of the doctors who helped draw up guidelines for vaccine priority groups also isn’t surprised at how things are unfolding.

The government’s vaccine advisory panel “did not expect vaccine police to be set up around the country,” said Dr. William Schaffner, a flu specialist at Vanderbilt University Medical Center, who is on the panel.