Controller / processor issue again ....

Company A is conducting research. Companies B C D .... hold personal data. Companies  B C D ... agree to pseudonymise the data they hold and submit the pseudonymised data to Company A.

Assume there is no problem with a legal basis - all subjects freely give fully compliant and informed consent.

Company A requires B C D ... to sign a data processing agreement acknowledging that in carrying out the pseudonymisation A is controller since it is determining purpose and method and B C D are just processors. Does that make ANY sense?

In the draft on my desk it leads to some bizarre consequences which A has clearly not thought through. For example one clause requires that B C D ...  limit access to the personal data to those carrying out the pseudonymisation which would mean that the data was unavailable to other staff for B C D...'s pre-existing purposes! Is it just that clause (and similar) which are wrong or, as I believe, regarding B C  D ...  as processors when they are working on their own data is a fallacy. 

PS Drafted by smart US lawyers ... 

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