It goes way beyond just genes and patient data. First, there's the issue of regulation. In most biology/psychology related fields, there's a raft of regulations from funding sources, internal review boards, the Dept. of Agriculture (which oversees animal facilities) and IACUCs for example that make it impossible to comply with this requirement, and will continue to do so for a long time. No study currently being conducted using animal facilities can meet this criteria, because many records related to animal facilities (including the all important experimental protocol) must remain confidential by statute (with the attestation of compliance from the IRB and IACUC). Likewise in the case of (any) human research, you'll have to get a protocol past the IRB for protecting subject anonymity, and given the likelihood of inadvertent identity disclosure that will extremely difficult to do.
Second, there's a deep flaw in how the policy is written and how it conceives of data. To wit, the policy defines: "Data are any and all of the digital materials that are collected and analyzed in the pursuit of scientific advances."
Now for starters, there's a loophole big enough to drive several trucks through: In many experimental contexts material necessary for complete understanding of the 'raw data' are not in digital form, but rather in say, lab notebooks. Which leads to the broader issue: what most researchers would be actually interested in seeing publicly disclosed is the 'data set' which is not 'raw data', but data that's processed into a useful, compact form that's suitable for statistical analysis.
However, in many experiments all of the material necessary to understand the 'raw data' (which I'll definite here as the measured result of an assay in a very general sense) is distributed between lab notebooks, digital data collection, calibration and compliance records in facilities archives and several levels of processing often using proprietary and very expensive software. Even if all of those things could be published (see above), the 'raw data' would be mostly worthless because of the vast amount of time and effort required in many cases to turn the 'raw data' into the 'data set'.
The third problem of course, which has been addressed in several places already on this thread is that there's no money in grants to fund the required repositories.
I think at some level this policy is a noble idea, but it's been implemented in a terrible way, and obviously written by people in fields that already have functioning, funded public databases. Either people are going to stop publishing in PLOS from many fields, or they'll drive the truck through the loopholes and it'll be just a toothless as Science and Nature's sharing requirements.
If they really wanted to effectively push for greater transparency, what they should be pushing at the moment is simultaneous publication of the 'data set', which would let fields that don't have standardized databases in place to design standards that would allow their creation.