That's one way of putting it. A rank of six implies that if all of the faces were represented by a matrix (e.g. with 20 rows, one for each face), the dimensionality of the column space would be six. That is, all 20 faces could be represented by linear combinations of six orthogonal faces.
OP implies that six "eigenfaces" faces represent an eigenbasis for the space of all 20 faces (that they are eigenfaces doesn't necessary imply that they form an eigenbasis, not every vector space has sufficient geometric multiplicity to have an eigenbasis).
It means that the faces can be described using only six uncorrelated parameters. Or to put it another way, there are only six axis of variations. Each face is a combination of the six eigenfaces, but there is still an infinity of different ways to combine these faces, and so an infinity of possible faces.
(Without a comparison to the general population, it's not obvious that 6 is a small number here, so take my "only" 6 cautiously)
I think it only means that each of the 20 faces can be composed from combinations of 6 "basis" faces. I don't know how that compares to the eigenface decomposition of 20 less similar people, I would imagine it is more a byproduct of the process itself than something meaningful?
Does this mean there are only 6 different faces shared among the 20 girls?