"come to lab"

Over at the Language Log, the Mark Liberman has posted a reference to a noun phrase he found interesting. The actress Amy Adams, speaking about a director, said "he'd just say hey, come to set, I want you to- to do something…"

The Liberman found the use of "come to set" to be analogous to "go to college":

And what struck me was Adams' inclusion of set in the class of singular count nouns that can be used in a prepositional phrase without a determiner, in a non-referential or generic interpretation: come to bed, go to college, stay in school, and so on...But this isn't quite enough — I don't think that even the most dedicated chemistry researchers would talk about "going to lab"...it seems that members of certain "communities of practice" extend this class of anarthrous status-nouns in community-specific ways."

The comments section has been relatively active and I posted a few points myself regarding "going to lab", leading to a bit of a disagreement regarding the relative referentiality of several minimal sentences.

In the interest of collecting some empirical evidence, does anyone see a difference in referentiality between the following minimal set:

(a) he'd just say hey, come to set, I want you to- to do something.
(b) he'd just say hey, come to lab, I want you to- to do something.
(c) he'd just say hey, come to college, I want you to- to do something.
(e) he'd just say hey, come to church, I want you to- to do something.

I don't think any of (a-e) meet the same non-referentiality of (f-g)):

(f) She went to college in the 1970s.
(g) He goes to church on Sundays.

I think I see a poster forming... PS; Carrie Niziolek has posted a set of "in lab" examples here.