Yes, Mary was the one with the claim to the throne. William refused to act as prince consort and they only agreed to take the throne if they could rule as joint monarchs.
The Michael Portillo programme on radio 4 was interesting. The thesis of the programme was that, as Brits, we see the "Glorious Revolution" from a purely British (or more accurately, English) viewpoint. Seen from a European perspective, it looks quite different.
Summarising wildly:
"Traditional version of history". Parliament and the country became worried that James's catholicism was going to drag the country back into the dark days of Queen Mary. A deputation was sent to Holland, inviting Mary and William to take over the throne. William brought a force over, the country rose to support him and James fled. An almost bloodless revolution had occurred and Protestantism was restored to the country.
"Alternative view". The two main European powers at the time were Holland and France, both of whom were squaring up for war with each other and casting about for allies. England was on friendly terms with France, and an alliance was a distinct possibility. William needed to neutralise this possible new enemy. Working with a group of disgruntled Protestants in parliament, he engineered the invitation. Once he received this , he landed with an enormous force, catching James off guard at the wrong side of the country. Realising the inevitability of a military defeat, James fled the country, leaving the country in Dutch hands. London was under Dutch military control for a matter of weeks, whilst William and Parliament rewrote the constitution (amongst other things, making it illegal for a Catholic ever to become monarch). Far from being "bloodless", this shift in the balance of power in Europe led to decades of war on the continent as well as prolonged war and continued grievances to this day in Ireland.
It was a fascinating programme and a good lesson in what happens when you see the same events from a slightly different point of view.