A proxy or cache doesn't substantively process the data. Here they are processing it if they are constructing anonymised models from it as you suggest may be the case. If they're processing it then they need to retain it long enough to perform those operations.

In the case at hand if they're processing it then they've "retained" it long enough to do that which is contrary to the spirit of the statement that it was 'fine that data was being sent to them as they weren't using it'. They used different words but this is the point of contention.

Either they discarded the data without further processing, amalgamation, statistical analysis, model construction, archiving or anything else or they used the data.

If they used the data in any way then it's a constructive lie even if there is some weaselling way in which their statement can be construed to be true.