idealweather that's not quite correct...you don't, in most cases, get to 'choose' what gets taxed where, it's usually based on what country the tax payer is resident in.
So, for example, a U.K. resident will be taxed under uk tax law on their worldwide income. Say they have a Spanish business interest, they will pay Spanish tax on that and will need to declare in Spain. They would not need to declare their UK income in Spain. They would, however need to declare their Spanish income in the UK as they are UK resident, and pay uk tax on this - however, they will gain credit for the Spanish tax suffered so the total tax paid will not exceed the highest amount of tax due on either country.
The issue in this case is the fund is a separate legal entity which appears to be resident in the Bahamas. The income arising from this for tax purposes is therefore the funds, not DC's family's and the U.K. has no taxation rights over this.
Exposure to uk tax would arise should David Cameron, for example, receive a distribution (I'm not sure how it's set up but assume it's a trust) from the fund; the distribution would be taxable in the uk and would need to be declared appropriately.
There is no evidence that this has not happened; the issue is the artificiality of the fund being resident in the Bahamas and thus avoiding tax on the fund income, rather than tax on the extraction of this income.
I think.