Generally I'd say if the data set is not shareable publicly then there isn't a good way of sharing in the context of public OpenRefine support. Note that while we have a group of people who commonly help debug issues, as a project I don't see that we could collectively take responsibility for the privacy of the data.
If the data isn't publicly shareable then if it were me I'd want some kind of formal agreement in place with any individual or organisation to ensure confidentiality etc. - basically a support contract in this context. Once that's in place then you could agree with that individual/org the best way of sharing with appropriate security.
The reason people request the data set when debugging is that they are trying to recreate the problem and narrow down the possible causes. Working with the data where the problem was originally observed is one way to narrow down the issue - because if it always fails for you with a data set, but works for someone else with the identical data set, we know that the issue lies somewhere other than the data.
So my first step, if I were you, would be to see if I see the same issue with another, shareable, dataset. If so, you can then share that dataset as the example. If not, then it seems likely that something about the original data set is causing the problem. In the latter case we get into more difficult territory because we now know the issue is with some configuration of data, but we don't know how to recreate. However that's a worry for if we get there. The first thing to establish is whether you see the same problem with some publicly shareable data - and if so, share that data on the issue
Best wishes
Owen