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I would not read this as questioning science but as the science-journalism equivalent of asking whether the 'mystery' can be 'solved' at all.

When a sentence is in form of 'Can X do/solve/manage/become/etc ... Y?' it is both simply asking and challenging X at the same time.

Challenging science is absurd as is challenging the reality.

"Can the president outrun a cheetah?" is not the same as challenging the president's qualifications as president.

It is challenging the idea that the president can outrun a cheetah, however. So, "Can science solve X?" is not the same as "Is science effective?".