“I think you can walk into the Dallas Museum of Art and see nothing that would cause concern,” Mr. Lane said.

Over the past decade, more than half a million students, including about a thousand from other Frisco schools, have toured the museum’s collection of 26,000 works spanning 5,000 years, he said, “without a single complaint.” One school recently did cancel a scheduled visit, he said. He did not have its name.

The uproar has swamped Frisco school switchboards and prompted some Dallas-area television stations to broadcast images of statues from the museum with areas of the anatomy blacked out.

Ms. Lawson and Mr. Reedy did not return calls. A spokeswoman for the school district referred questions to the school board’s lawyer, Randy Gibbs. Mr. Gibbs said, “there was a parent who complained, relating the complaint of a child,” but he said he did not know details.

In the May 18 memorandum to Ms. McGee, Ms. Lawson faulted her for not displaying enough student art and for “wearing flip-flops” to work; Ms. McGee said she was wearing Via Spiga brand sandals. In citing the students’ exposure to nude art, Ms. Lawson also said “time was not used wisely for learning during the trip,” adding that parents and teachers had complained and that Ms. McGee should have toured the route by herself first. But Ms. McGee said she did exactly that.

In the latest of several statements, the district contended that the trip had been poorly planned. But Mr. Gibbs, the district’s lawyer, acknowledged that Ms. Lawson had approved it.

“This is not about a field trip to a museum,” the principal and superintendent told parents in their e-mail message Wednesday, citing “performance concerns” and other criticisms of Ms. McGee’s work, which she disputes. “The timing of circumstances has allowed the teacher to wave that banner and it has played well in the media,” they wrote.