It's been a contentious question since the day Bethesda picked up the license. There's no denying that Beth has kept the series alive, but as naossano says, there were numerous others spoiling to do so. Most of them would probably have stayed truer to the original series' core principles and design, as well.
Whether such an effort would have been able to achieve the kind of commercial and critical success Bethsoft did is an issue of opinion and speculation, but it's highly unlikely that any of the other serious candidates for the license would have released their version of F3 to outright failure, and regardless of whether they would have brought in such huge sales figures or attracted quite as sizable a new audience of console kiddies, there's really very little doubt that Fallout would have survived (and thrived, though perhaps not turning AAA numbers) to this day no matter who picked it up.