I'm simply trying to make the point that, considering her Health Committee role, she should have known the veracity of the £350m claim far earlier than most
The £350M figure is the amount the Brexit campaign have been claiming is the net amount we pay the EU. It's false because it does not account for the UK's rebate, and does not account for money the EU returns to the UK in the form of investment. It's actually the amount that hypothetically would have been our net contribution if we didn't have a rebate and the EU spent nothing in the UK.
The Brexit argument that this amount would be available to spend on the health service is also not plausible because, even if the figure for our net contributions was correct, it doesn't take account the likely loss of taxation revenue that would result from the economic hit from leaving the EU. That amount is unknowable but most economists seem to agree that it would be substantially greater than our net contribution, so the overall result would be a net loss in money available, not a net gain. Further, it assumes that, if the amount became available, the UK Government would actually choose to spend it on the health service. Judging by the record of the present Government, that seems unlikely. Tax cuts for the wealthy seems to me rather more likely.
But the key point in response to your comments is that none of that information requires any particular knowledge of the health service, so it seems unlikely that being on the Health Committee would make it more likely that an MP would know it. On the other hand, it is all fairly basic stuff, so you'd have thought any reasonably well-informed MP would have been aware of it. If Sarah Wollaston didn't know all that two months ago, then I'd agree with you that she would seem to have been somewhat badly informed for an MP.
Still to my mind, a late understanding of reality is better than no understanding of reality at all
