Lees-Galloway granted residency to Sroubek in September, but reviewed the case after it emerged that Sroubek may have travelled back to the Czech Republic, and following reports that his estranged wife no longer supported his residency bid.
After the review, Lees-Galloway issued a new deportation notice to Sroubek, who is appealing it.
The Minister said on Friday that if he had evidence that Sroubek had gone back, he would have "likely" decided to deport Sroubek from the outset.
But National Party immigration spokesman Michael Woodhouse said the minister was clutching at straws because, even disregarding whether Sroubek had been back, the case against him was so strong that the minister should have decided to deport him immediately.
Woodhouse added that the Minister should have just asked Sroubek the "obvious" question about whether he'd been back, if that information was so vital.
Lees-Galloway said that he did ask, but immigration officials told him the information could not be ascertained.
Immigration NZ's system did not show Sroubek's travel to the Czech Republic because it only records a person's flight into or out of New Zealand, but not the starting point or end destination.
Despite the minister's query, Dunstan confirmed that officials had not asked Sroubek if he had been back.
"The preparation of case files does not currently include an investigative role and therefore there was no requirement to put the question about his alleged travel to the Czech Republic to Mr Sroubek," Dunstan said.
"However, the question of whether Immigration NZ should take on an investigative role when preparing case files will be addressed as part of the current review being undertaken by Mike Heron QC."
Dunstan said the travel information in the 2012 email about Sroubek's travel history was unverified.
"As the original case file made clear, Mr Sroubek's immigration history is not clear cut and it appears he may have travelled in and out of New Zealand using more than one travel document.
"Immigration NZ were focused on information that was relevant to the grounds under which he was liable for deportation."
After Lees-Galloway ordered the review, however, officials asked Sroubek and he confirmed he had been to the Czech Republic twice in 2009 - under the name Jan Antolik.
Asked if officials had failed him in this case, Lees-Galloway said on Friday that he will await the findings of the review.