You must have not read it very well then:
Palestinian-Israeli Relations and the Peace Process: Support for the two-state solution stands at 44%, while 50% oppose it—virtually unchanged from ten months earlier. Yet support for a specific two-state formula based on the 1967 borders is considerably higher, at 56%, including 61% in Gaza. Confederation receives 14% and a single democratic state with equal rights 10%. At the same time, 58% believe the two-state solution is no longer practical because of settlement expansion, and 64% see little or no chance of an independent Palestinian state emerging within five years.
You'll notice that the 44% (and 56% with 1967 borders) support for a two state solution is significantly more than the 10% for a single state with equal rights. You'll also notice that the above exert says mostly the same thing as that Pew Research poll you linked.
But yeah, accuse me of lying about what Palestinians believe by providing a source that asks a different question. 'Do you want a two state solution' vs 'do you think a two state solution is realistic' are not the same question, nor is the latter evidence that Palestinians want a one state solution like you originally claimed.