Polls on CBC's independence

No sooner do I complete my June paper (a 15,000 word research design for the thesis), than I find a new data point on perceptions of political independence by the Friends of Canadian Broadcasting.

The first poll is by Ipsos-Reid, and asks

Thinking specifically about the CBC...which of the following two statements is closer to your own opinion?

Statement	May. 04	Aug. 02
The Prime Minister’s power to appoint the CBC President and Board of Directors gives the government too much influence over the nature and content of programs broadcast on the CBC	45	46
The CBC is independent and it doesn’t matter who appoints the Board of Directors and President	52	50
Don't know/no opinion	3	5

The poll is poorly worded, since the options are not mutually exhaustive. One might think CBC is independent, but it still matters who appoints the Board of Directors. (It reminds me of the get-out-the-vote campaign in West Wing, Season 4, where will changes one kid's sign from "It doesn't matter who you vote for, make sure you vote", to "No matter who you vote for, make sure you vote").

A similar question was asked in 1999 by a different polling group (Compass); at 35%, the percentage replying "independent" was much lower.