Buying into an ETF is buying into a company that owns shares. The ETF owns the shares in other companies, you own shares in the ETF. You do not own the shares that the ETF owns.
Similarly, if you buy shares in Apple, you do not directly own its cash, facilities, intangible assets etc. Apple owns these. But you own voting rights and the ability to participate in dividends or buybacks.
In both cases the company -- the company's management, really -- has a wide degree of freedom in what it does. Apple can buy companies or sell iPhones without consulting shareholders. ETFs can buy and sell shares similarly.
Similar-looking but quite distinct is the trustee/beneficiary relationship from trusts law. In that case the trustee legally holds property "for the benefit of" the beneficial owner. Again, as a beneficiary, you would not own the shares held by a trust on your behalf, but the trust would need to buy and sell them according to its view of your best interests.
Since both corporations and trusts have wide-ranging legal, financial and taxation implications, the details vary widely depending on where you are. Each jurisdiction has comparable but distinct caselaw and of course legislatures have tinkered quite feverishly with it too.
I am, of course, not a lawyer. I didn't even finish law school.