That sounds nice, but it's a load of baloney. I would wager that most people over the age of 20 (25?, 30?) have experienced a significant relationship(s) where the sex tends to be passionate (and frequent) at the very beginning, and tapers off and becomes less frequent, less passionate, more boring as time goes on (and years drag by). In fact, that is the typical progression of sex in a committed, caring relationship. So, no, I would not say that the key is "actually caring about the person".
I haven't read the linked article yet, but the subject reminds me of some work done by a psychologist named David Schnarch, who has built a career and written several books on the subject. These include a book called _Passionate Marriage_, intended as self-help for a lay audience, and _Constructing the Sexual Crucible_, which is more of a technical handbook for therapists and counselors.
See http://passionatemarriage.com/
http://passionatemarriage.com/catalog/15
Alain de Botton also examines the issue in a similar way on the impressive "Book of Life" website. E.g., he says:
"In a wiser world, we would collectively admit that the very rare cases where love and sex did run together were astonishing exceptions with no relevance whatsoever to most of our lives. We would instead learn to pay admiring attention to those who had accepted with a reasonable show of dignity and grace that the natural price of long-term togetherness is a decline in the quality and frequency of sexual contact – and that this is, in a great many cases, a price very much worth paying."