"Twice before the video starts, his dad had to hold him and pulled his arms up in a V-shape to allow the TSA agent to continue," he told The Salt Lake Tribune.
The father pulled the boy's shirt off "in frustration," prompting an agent to shout, "Sir, sir!" Tait said.
In a statement posted late Sunday to the TSA's blog, a spokesperson wrote that the father removed the boy's shirt "in an effort to expedite the screening."
"No complaints were filed and the father was standing by his son for the entire procedure," the blog states.
Tait said he walked toward the father and son to talk with them after agents sent them into the terminal, but a man in a dark suit pulled him aside. The man had just been speaking with TSA agents, Tait said, but he did not show a badge or identify himself.
"He started to question me: 'Why was I recording the procedures of TSA?' 'What are your plans with this video?' " Tait said. "I said it looked like something was going on; I never [before] saw a shirtless young boy getting patted down."
The man then told Tait to delete the video in front of him, arguing the video invaded the family's privacy.
"I said, 'I'm not going to do that,' ... and left for my gate."
As for the removed shirt, the TSA statement stressed that passengers were not asked to disrobe.
"You should not remove clothing (other than shoes, coats and jackets) at a TSA checkpoint," the blog states. "If you're asked to remove your clothing, you should ask for a supervisor or manager."
Tait's video, which had been viewed nearly 190,000 times on YouTube as of Sunday night, was posted on the heels of debate over whether pat-downs and full-body scans are invasive security measures.
TSA head John Pistole last week defended the pat-downs against criticism that travelers should not have to submit to full-body scans or submit to a pat-down, including over-the-clothing contact with the subjects' genital areas.
"Clearly it's invasive, it's not comfortable," Pistole said of the scans and pat-downs during an interview on CNN's "State of the Union." But, he added, "if we are to detect terrorists, who have again proven innovative and creative in their design and implementation of bombs that are going to blow up airplanes and kill people, then we have to do something that prevents that."
The Associated Press contributed to this report.