MOST ABSOLUTELY NOT!!!
Sorry, but it infuriates me when people have been mislead and henceforth don't treat their fish correctly.
No fish enjoys small spaces, least of all a betta. You unfortunately, where ever you go will find pet shops keeping betta's in tiny little cups with barely enough room for them to spin around in. This is an act of vulgarity, never to be copied. The person that told you was no doubt a salesman, who was trying to keep the stores reputation by telling you that they require no space to move.
My reccomendation...would be to buy a tank no smaller than 5G for your betta, which is bare minimum in my opinion, although my betta's tank is a 10Gallon.
Hope that helps:)