Apparently (so I am told), hiring someone to do the book-keeping for a company is not sufficient care in making sure the books are kept properly. Just seeing that witholdings are showing up on pay slips and assuming they are being remitted is not enough. Instead, the director is expected to track down and be sure that the remittances are being done (because they are liable for them if they are not).
That's a bit difficult to do if you never get a chance to see the books, but the idea is apparently that if you (as an employee or shareholder) are accepting the cheques then you (as a director) are considered to be required to have audited the books. You are expected at least to have not cashed your own salary cheque until you've made sure that the government got their slice.
Also, it really doesn't pay to be patient in these cases. Letting someone string you along for years with promises to get the books up to date and in your hands means that hundreds of thousands of dollars of personal liability can pile up for the directors.
[Update: seems a directorship is an official capacity for a company, not something you can just fall into. AFAICS right now I never actually became a director.]