They could be a shelf full of $2 novels. Owning a few hundred books doesn't cost very much (thanks printing press), and only implies an interest in reading not in being of a high socioeconomic status.
In context of the article as anecdata, I don't think the books themselves had anything to do with mine or my brother's successes. We never even read any of them. It was more of a reflection of what my parents were interested in, which obviously had effects in how we were raised.
http://www.nydailynews.com/life-style/average-american-watch...
Beyond that, though, it's not merely the case of an individual having time to read. A parent who does not read to their child is raising a child to be less literate or even illiterate.
Where did you get this idea? It's certainly not accurate in the US.
The general phenomenon here is very well known; just searching around for this I found stuff like "UK time use data for the period 1961-2001 do indeed indicate a reversal of the previously negative leisure/status gradient". ( https://www.iser.essex.ac.uk/files/iser_working_papers/2005-... ). But that paper is obviously more concerned with the UK than the US.
Data on this is directly available from the American Time Use Survey, if you want to tabulate it yourself -- while they do collect various data on employment status, they don't publish a summary of time use by employment status.