Forgive me, I am forgetting my basic statistics.
Treating Likert data as ratio would be bizarre as there is not a natural zero point. You could, for example, translate the entire scale by any constant and the meaning would be the same.
The "interval" approach is very common in the literature I am most familiar with (psychology). However, I cringe when reading a paper that treats Likert data as interval, because there is probably a different psychological "distance" between the upper end points of a scale than between middle end points. I am not aware of psychological research to this end specifically using Likert scales (although such studies surely must exist), but similar psychological distortion of continuous measures occurs in other settings. For example, subjective judgments of the probability of some event are not linear with respect to the event's actual probability. Instead, events with probability near the endpoints of the scale (0% and 100%) are perceived as regressing to the midpoint (50%). I will see if I can track down the reference for this.
That leaves us with ordinal and nominal. Ordinal requires the assumption that the scale is perceived as 5>4>3>2>1, for example, which appears reasonable. An approach I have used is to look at the proportion of some response of interest, such as "agree" and "strongly agree." You will have less power using such an approach than if you treat the scale as interval, but I consider this an inherent drawback to these types of scales.