By Juana Summers

(CNN) -- Former Veterans Affairs Secretary David Shulkin has repeatedly insisted that the White House fired him from his job at the department. The White House says Shulkin resigned.

Which of those two things actually happened could have sweeping implications that could throw an agency beset with challenges even further into turmoil.

When President Donald Trump announced on Twitter last week that Shulkin would depart the agency and that a Defense Department official, Robert Wilkie, would serve as acting secretary, he side-stepped Shulkin's deputy, Thomas Bowman, who was next in the line of succession. That decision has given new life to the legal debate over how a President can pick a replacement for departing Cabinet secretaries.

What is the Federal Vacancies Reform Act?

The Federal Vacancies Reform Act of 1998 gives the President the authority to temporarily fill a vacancy at a federal agency if the official "dies, resigns, or is otherwise unable to perform the functions and duties of the office."

The law, however, doesn't explicitly say if the president still has that authority if the person is fired.

What could this mean legally?

If Shulkin was indeed fired, Trump's decision to replace him with Wilkie instead of following VA's line of succession, could imperil any decisions Wilkie makes while serving at VA in an acting capacity. There could be legal challenges to any actions that Wilkie makes, at a moment where VA is at a crossroads and decisions are looming about some of the department's biggest functions.

Given the lengthy process for Senate confirmation, Wilkie could serve in an interim capacity for months.

Trump nominated White House physician Ronny Johnson to become the VA's next secretary, but lawmakers and veterans' groups have raised questions about whether or not he has the right experience to lead the government's second largest bureaucracy.

A challenge to Trump's pick of Wilkie could also be an attractive opportunity for groups that oppose the Trump administration's policies. An environmental watchdog group, Public Employees for Environmental Responsibility, is taking that approach with a handful of Interior Department nominees who it says have been in their temporary roles longer than the law allows.

What is Shulkin saying?

Shulkin has repeatedly said that he did not resign his job, and never wrote a resignation letter. He said he actually spoke to the President himself the day he left the VA, and that no mention was made that he would soon be out of a job.

He told CNN he learned of Trump's decision to make a leadership change at VA from a phone call from White House chief of staff John Kelly, prior to the President's tweet.

"I came to run the Department of Veterans Affairs because I'm committed to veterans, and I'm committed to fighting for them," Shulkin told CNN's Jake Tapper on "State of the Union" Sunday. "And I would not resign, because I'm committed to making sure this job was seen through to the very end."

What is the White House saying?

Over the weekend, the White House insisted that Shulkin had resigned his job.

But on Monday, White House communications aides framed it differently, with Mercedes Schlapp telling Fox News that Kelly "called Shulkin and gave him the opportunity to resign."

"Obviously the key here is that the President has made a decision. He wanted a change in the Department of Veterans Affairs," she said.