That is true of independents, but Romney's problem was not with independents. It was with Republicans. That tells me that your supposition is intrinsically wrong with regard to Romney.
As more vote totals have come in, Romney has gotten pretty close to McCain's number of votes. He's 1.5 million under McCain, while Obama is 8 million under his 2008 totals. And just matching McCain's numbers would now leave Romney with a 2 million loss.
The fact remains that Romney got millions of Obama's voters to stay home, but couldn't get them to show up and vote for him. Whatever their party ID was, and it could've changed between 2008 and 2012, the task was to get former Obama voters to vote for Romney. Obama's 2008 win was so huge, there was no other way to win. So Romney didn't have a problem with Republicans, but with people who were wishy-washy enough to have voted for Obama once already.
As for the independents who did show up, Obama won I's by 8 last time, Romney won them by 5 this time. So we could have used more of the I vote. Romney went up with R's by 3 points, but went down with D's by 3 points, so kind of a wash there. The percentage of party turnout stayed about the same as in 2008, so the electorate declined evenly among all 3 groups. So, in that sense, there were both R's and I's who stayed home that we could've used.