The Sports however claims that Town were in the bidding for the 21-year-old and it was only Swindon's ability to offer a fee that swung the deal their way.
Paul Groves has previously said that all his budget has gone, with Iffy Onuora the final signing.
The ruling out of Jonny Rowan for three months may have forced Groves to ask for more money from the board. Especially with his reluctance to use Phil Jevons.
Fallon played 18 times for the Tykes this season, scoring four goals. He came on as a sub in the 0-0 draw at Oakwell last month.