Actually, the RM is quite clear on this.
"Within" means the base must be at least touching the edge of the effect range (note this means the rest of the base can be past the effect range, see diagram page 37).
"Completely Within" means the base must be completely within the range of the effect.
As for placement effects in particular (and the text referenced in the initial post):
"A model's base must be placed where it can fit...." means you can't place the model where there isn't physically enough space for it to occupy (due to terrain, other models, etc.).
"....and may not be placed so that any portion of it is further than the placement effect permits." This refers to either "within" or "completely within", as dictated by the specific placement effect used at the time.
"Unless stated otherwise, a model's base must be placed completely within any stated range." If the specific effect being used by the character does not say otherwise, the default for the placement effect is "completely within".
In the example you gave for Dreamer, yes, it overrules the default restriction of "completely within" for the placement effect. This is evident from not only the exceptions noted in the placement effect rules on page 38, but also in the "Breaking the Rules" section on page 7.