I think they might be obscuring the underlying issue. Their data should reflect the full text use by your patrons on their site regardless of what linking path they took to get there.

What they seem to be saying is that your patrons may be accessing some of their articles entirely on other platforms. In that case, that full text usage should NOT be "credited" in terms of calculating cost per use to the subscription that you pay them. Or they could be blurring the difference between full text usage and session/search usage. Of course if your patrons are searching on another platform and just link directly into the full text on the publisher's platform, only a full text use, not a session or search, may be recorded.  That's one reason I totally ignore session/search data for platforms that we consider primarily as repositories of full text, like most publisher platforms, and only consider that data for products that we actually subscribe to for the indexing itself, including our discovery service, A&Is etc.

Melissa