If denied boarding, this traveler at Newark Liberty International Airport would be entitled to swift compensation. (Julio Cortez/AP)

Is your airline telling you everything? After a government operation that netted four airlines, the unsurprising answer is: No.

Last year, the U.S. Department of Transportation (DOT) dispatched plainclothes investigators to a dozen American airports under the code name “Task Force Lightning.” When it comes to the proper treatment of air travelers, regulators wanted to ensure that airlines’ front-line employees knew the rules.

Many didn’t.

Alaska Airlines, American Airlines, Southwest Airlines and United Airlines failed the surprise inspections, incurring small, but embarrassing, fines from the DOT’s Office of Aviation Enforcement and Proceedings.

A closer look at the enforcement actions, which were issued in August, points to a truth about flying that you can pack on your next trip: Even the most reliable airlines often can’t be trusted to tell you everything.

The investigation covered compliance with a wide range of rules, including denied-boarding statements and liability limits for lost luggage. If your flight is oversold and you’re denied boarding, your airline is usually required to compensate you on the spot — or within 24 hours, under certain circumstances — with cash or a check. The amount varies based on the length of your delay and whether your flight is domestic or international. Currently, that amount could be up to $1,350.

When it comes to luggage, federal regulations say an airline may not limit its liability for provable direct or consequential damages resulting from the disappearance of, damage to or delay in delivery of a passenger’s baggage to an amount less than $3,500 per passenger. The DOT publishes these rules in its helpful online brochure — FlyRights — which can be found at airconsumer.ost.dot.gov/publications/flyrights.htm.

Consider Alaska Airlines, an air carrier whose customer-service scores are among the industry’s highest and which has an enviable reputation. Its agents failed to produce current copies of the airline’s written denied-boarding statement. On several occasions, employees showed DOT staff outdated copies of the denied-boarding statement that listed compensation amounts which were, in some cases, as many as five years out of date. Also, signage at certain airport ticket counters and boarding gates claimed that the airline’s domestic baggage liability was limited by regulation to amounts of less than $3,500.

Alaska Airlines was fined $40,000.

How about Southwest, another carrier with a clean reputation when it comes to service? During compliance inspections, some of its agents failed to show up-to-date copies of Southwest’s written denied-boarding statements. One agent in Oakland, Calif., offered “only a partial copy” of the statement, which contained compensation amounts $25 to $50 below the actual amounts.

Like those at Alaska Airlines, Southwest agents in Salt Lake City produced ticket notices or displayed signage at some airport ticket counters that purported to limit the carrier’s domestic baggage liability to amounts less than $3,500. Some of the information offered by the agents was more than three years out of date, according to the DOT.

Southwest was fined $40,000.

The presence of American and United will probably come as less of a shock. And American’s rap sheet will look familiar by now. It includes failing to produce a denied-boarding statement and offering outdated statements, some more than five years out of date. Total fine: $45,000. Ditto for United, which is said to have been unable to show copies of its denied boarding statement at either the ticket counter or the boarding gate. It also produced outdated copies of the statement. United was fined $35,000.

In the DOT consent orders (directives adopted to avoid litigation) the airlines issued boilerplate rebuttals that say they take their obligations to provide accurate information seriously and are committed to delivering a positive travel experience. Taken together, however, the documents suggest that while airlines are required to offer information about compensation for denied boardings and lost luggage, they may not always do so.

Air travelers say “Task Force Lightning” is a good start, but they want to see more.

“The government should have the airlines go back and identify every instance where incorrect information has been provided and correct it,” says Joe Farrell, a lawyer and frequent traveler from San Antonio Heights, Calif. “That would be a meaningful exercise of regulatory power. Fining them chicken feed results in behavior that is no different.”

Others agree that the fines were not enough.

“I’m not sure that’s much of a deterrent to airlines,” agrees David Brakebill, who works for a nonprofit organization in Key West, Fla. “If the DOT were serious, they’d have fined them in the hundreds of millions.”

But insiders at the DOT, speaking on the condition of anonymity to speak freely, say the goal of its task force was educating frontline airline employees, rather than just managers and executives at headquarters, and they tell me “Lightning” may strike again, with more plainclothes investigators at airports.

For the time being, check to see what your rights are when your flight is delayed or your luggage is lost.

Your airline may not be a reliable source.

Elliott is a consumer advocate, journalist and co-founder of the advocacy group Travelers United. Email him at chris@elliott.org.