It's not really a rationalisation, it's explicit in the charcter, Tim never wanted to be Robin and when he took on the role it was out.
He knew Batman needed a Robin because he'd seen in the news how Batman acted when he had a Robin, and how out of control he'd become after Jason's death.
With Jason gone that left only, in Tim's mind, Dick as a possible Robin and that's the path he rather single mindedly employed until the first time he put the costume on.
And at the same time, though he knew the public perceptions, he didn't know the real dynamics between Dick and Bruce as people.