Here's the quick and clean answer to your question, though one that will probably leave you rather unsatisfied if you're unfamiliar with yogic philosophy: meditation (dhyana) is the seventh of the eight limbs of yoga (ashtanga here meaning "eight limbs", not to be confused with the active style of yoga of Sri Pattabhi Jois, sometimes spelled "astanga"). The ultimate goal of Yoga (notice the capitalization) is samadhi, or enlightenment, which is the eighth limb. All the limbs (yama, niyama, asana, pranayama, pratyahara, dharana, dhyana and samadhi) all lead from one to the next in succession to that ultimate goal. These are techniques for proper living ethics between yourself and others, yourself with regard to yourself, practices involving the physical body, breath control, sense control, concentration, meditation and then ultimately, bliss. So that's the big picture answer to where meditation lies with respect to the complete practice of Yoga.

A more subtle answer to why we should want to steer away from reacting to the wavering thoughts of the mind is that that is exactly the technique employed while in concentration, which leads to meditation (6th and 7th limbs, respectively). "We are not the body, we are not the mind." We are the capital "S" Self that is beyond the scope of the senses and the thinking mind. Being in the present moment, which is the technique you mentioned to achieve concentration, is exactly just that: a technique. It's very difficult to keep this big picture viewpoint in mind while focusing on each individual goal and technique employed in the practice, which is why emphasis is usually given to each technique itself as a goal unto itself. Work on the techniques with the proper attitude and the goals should follow of their own accord is the thought process behind the teachings.

Did I confuse you more? Don't say I didn't warn you!

Great question, btw.