The 747s, in fact, belong to Evergreen, a U.S.-based international aviation contractor, which flies equipment and troops for the U.S. military.
The company normally uses Germany for its stopovers to places like Pakistan and Afghanistan, but last week its planes were diverted to Malta since the skies over mainland Europe were declared out of bounds because of the volcanic ash cloud crisis.
After the alert was raised, two department officials inspected two aircraft last Wednesday - the day they landed for what was meant to be an overnight stay.
There was nothing untoward with the cargo, which turned out to be nothing more than "very sophisticated" communications equipment, but the officials still felt Evergreen needed an export licence for it, even though the planes were not loading or unloading in Malta.
The red tape meant the planes were effectively grounded for an extra two days, but not just because of local procedures.
One of the aircraft, which was due to leave on Thursday, had to stay put till Friday because in the meantime its papers for Turkey had expired.
But even then it could not depart at its allotted time of 3 p.m. since the crew were held up in traffic caused by a major traffic disruption in Marsa which caused several delays at the airport.
Evergreen was planning more stopover flights in the coming weeks but cancelled its plans after what happened, according to Malcolm Camilleri, the managing director of the company that took care of its ground handling.
"There wasn't a programme of flights as such. These are technical flights and are not as predictable. But we were given the indication that more flights would follow and now they will not," Mr Camilleri said.
He would not be drawn on the intervention of the authorities. "I would need to know the details to comment and I don't have those details because we simply provide the ground handling, so the Customs Department owes us no explanation. However, if we lost this business due to red tape it would be a pity," he said.
"Overall," he added, "I get the impression that this sort of business is not given importance despite the fact that Malta International Airport makes an effort to promote it. It seems like all the importance is given to aircraft that carry tourists."
Asked for a comment, the U.S. Embassy said it was aware of the flights but pointed out that it was not tracking the commercial flights and was not involved in supporting the aircraft's operations during its stopover in Malta.