You are right, William III needed Mary II. Now I remember reading that Mary II actually begged the parliament to offer the throne to her husband. Too bad she was so weak and never had much to do during her reign. I wonder what kind of a de facto monarch would've she been...
The Parliament was divided into three fractions those day; one believed that Mary had to be Queen in her own right, while William could be King of England in her right, like Mary I and Philip of Spain (that would mean he wouldn't remain King if Mary predeceased William). That idea seemed to have most support in the Parliament.
The other, smaller group, wanted William to be King in his own right, while Mary would be his Consort, not Queen Regnant, like Henry VII and Elizabeth of York (Elizabeth, who was the Yorkist heiress to the throne, had considerably more rights than Henry).
The third and probably smallest group proposed that both Mary and William should become Monarchs, with the surviving one continuing Reigning until his/her death (that was unprecedented in British History, for although Philip of Spain was King of England, he was King only in his wife's right and couldn't remain one after her death).
The majority of Parliament still wanted Mary to be the sole Sovereign, with William as a King as long as Mary was alive. However Mary, loyal to her husband's interests, repeatedly declined the offer and insisted she wouldn’t agree to become Queen if her husband wasn’t a King Regnant (William himself refused any other outcome).
In the end, the Parliament came up with the Bill of Rights 1689, which satisfied everyone:
* Mary and William were to be joint Rulers, and the surviving one was to continue to Reign until his/her death
* In the line of the succession, precedence was given to the children William and Mary could have, followed by the children Mary could have from any later marriage
* In case their marriage was childless, Princess Anne and her Heirs were to succeed them (not succeed Mary, but the surviving Ruler, which turned out to be William)
* Recognizing William's rights, his Heirs from a later marriage (to a woman other than Mary) would be directly beneath Anne's Heirs in the Line of the succession
If Mary were a stronger woman or a less devoted wife, she could have become a sole Monarch without significant opposition.