This seems to be a curious question.  I don't see any problem with getting IDP credit at a LLC, solely based on their registration status.

NCARB and IDP are operated independently of the state, and you can earn a number of IDP credits whether you're under an architect, engineer, or "under the direct supervision of a person experienced in the activity" (limits on each category of course)..  The question might be whether the type of work is qualified as work "Category A" under IDP.

Now, since IDP 2.0 rolled out, if I'm not mistaken, there was a change of language describing "Category A" where it was defined along the lines of "a firm engaged in the comprehensive practice of architecture"  (comprehensive was dropped), so it might be that at the time the firm wasn't engaged in all facets, and it was called into question.

The more likely scenario, is that it had nothing to do with IDP, but rather New York States own Experience Requirement. Now you have a category I and J to compete with, and you'll see that LLC is not on their list of "Category I" requirements.  

That's what I am talking about. Would my experience in NYS count if I have worked at an LLC?

It will count, but only to a point.  Note this section from the above link:

Applicants with credit in Categories A and F must document at least two units of experience in Category I.
Applicants in Category C must have at least four units of experience in Category I.
Applicants in Categories D, G, and H must have the majority of experience in Category I.

So you'll need to see your education category (A-H), and match it here for the minimum time at an employer in Category I...  Now it also says "with few exceptions," so you could very well argue that your employer should be or is an exception (I'd hate to have that fight).