Keep in mind the way they're defining "white noise" in the scientific american article you provided is different from what you link to on wikipedia. The SA definition is more in terms of ambient noise (e.g., traffic, low-level talking, a/c running, etc.) while white noise proper is a signal with a VERY specific acoustical pattern. It seems that the SA article is relating to deterioration in performance due to the stress caused by the increased attentional resources required to "tune-out" the ambient noise. If white noise proper completely eliminates all other ambient noise (without being too loud of course), this eliminates the allocation of these additional resources. Because white noise proper is essentially featureless, one will habituate to it unlike common ambient noise.
Carlson, Rama, Artchakov, & Linnankoski (1997) found a significant decrease in memory when exposed to music during a memory task and a significant increase in performance when exposed to white noise in comparison to a control which had only low level ambient noise. Though it was not the main purpose of the study, the authors conclude that music drew attention away and thus interfered while white noise likely drowned out the ambient noise without drawing attention and thus improved performance. Please keep in mind the sample of this study was on monkeys, but the processes are expected to be generalizable to humans.
Daee & Wilding (1977) found that the likelihood of forgetting during a free recall task is related to the level of noise to which one is exposed during rehearsal such that recall is best in a quiet environment and degrades at 75 and 85 dB. Though this study was not on concentration directly, these results can be seen to have applicable implications regarding attentional resources.
Along these same lines, Salame & Baddeley (1987) found significant differences in recall between unattended speech versus white noise such that unattended speech interferes with performance while no statistical difference was found in the white noise condition (in comparison to a quiet control). The authors conclude "...that noise does not interfere with short-term memory but that unattended speech does impair performance..."
The studies I cite above are related to memory recall tasks which, though involving similar processes to long-term concentration are not perfectly comparable. However, there is a pretty comprehensive literature showing the effects of noise exposure having negative effects on long-term tasks such as learning (e.g., Hygge, 1993, Lercher, Evans, & Meis, 2003). Additionally, Mathews & Canon, 1975 state "data [suggests] that arousal leads to a state of restricted attention or cue utilization in which attention is concentrated on salient features of the setting at the expense of its other aspects" which does not hinder attention to "central or salient events." This idea is related to the theory that noise facilitates functioning through the stimulation of processing such that increased arousal yields better performance until over-arousal occurs which then decreases performance (Hockey, 1983 from Staal, 2004). Stall (2004) also discusses the possibility of continuous v. intermittent noises having differential impact such that continuous may be beneficial while intermittent is harmful, though there is no current agreement in the literature (see pages 88-91).
Thus, the literature seems to support the following:
White noise will improve performance to the extent to which it masks noises that may cause over-arousal or attention shifts away from the task without causing over-arousal itself. Practically speaking, if you're in a quiet environment, white noise is unlikely to have a positive effect on your concentration. If you are in a somewhat noisy environment, white noise will likely have a positive effect. However, in a very noisy environment it will likely have either no or a negative effect.