Did they really think, after nine Tests, he could not cut it at the highest level? Or was it that someone within the England hierarchy felt that the bowler's relaxed approach did not reflect the positive, thrusting image they were seeking to promote?
Languid and easy-mannered, the 28-year-old from Southend via Perth does not always come across as a driven man, much as he insists the impression is misleading. However, the proof of ambition is now visible - not least in his chest measurements.
Last summer ended with a knee operation but since then Mullally has worked single-mindedly towards regaining his Test place.
"I could not play any cricket until February but I worked hard to improve my fitness and to put right the things it was suggested I put right last time I was with England," he said.
The evidence can be seen in a shortened run-up and a broadened upper body. After much pumping of weights back home in Perth, the 6ft 5in former beanpole stretches the tape measure to 46 inches across the chest, compared with just 42 last year.
"My team-mate, David Millns, reckoned I was sharper off a shorter run so I have cut it down by six paces," he said. "That has given me a lot more balance at the crease, which helps with accuracy. I've also worked on getting closer to the stumps without running on the wicket in the follow- through.
"I'm pretty pleased with how it has gone so far. Without wanting to blow my own trumpet, I feel I'm bowling better now than at any stage in my career.
An eight-wicket return in Leicestershire's Championship win over Gloucestershire and another clutch of wickets against Hampshire bear witness to that. And if the England selectors have not yet noticed they might consult Wasim Akram, who was impressed when Lancashire met Leicestershire in the Benson and Hedges Cup.
"He said he thought I was looking good off the shorter run," Mullally said. "Coming from him that meant a lot to me."Reuse content