The fact that the hardship distribution "reimburses" an expense that has been paid does not necessarily mean that the hardship is no longer there or that the participant should not be able to utilize a plan feature.
For example, I have 2,000 disposable income until my next paycheck, of which I need at least $1,500 to cover expenses. I end up with a medical emergency and I need to pay the hospital $1,000. Knowing that my 401(k) plan allows for hardship distributions, I pay the $1,000 from my checking account and apply for the hardship to "reimburse" myself for the expense. The medical bill has been paid, but without the hardship distribution, I can no longer cover my expenses. Do I not have a hardship because I used the money in my checking account to pay for the bill?
I asked a similar question a few years back at the ASPPA annual IRS Q&A. The issue was that most of the hospitals in my area are requiring payment for services before you leave the hospital instead of the old approach of a payment plan. If you cannot pay your bill, they will set you up with something like MedMax, Care Credit, or some other type of financing. In the end, the hospital is paid in full, and the patient walks out with an open line of credit that will take you to court and destroy your credit if payments are not made.
Long story short, we started seeing a lot of hardship applications to pay off these medical credit lines. The question then becomes is it still a hardship if the bill has been paid through other means, in this case a medical credit line or a credit card.
The answer from the both the ASPPA panel and the IRS was that what triggered the eligibility for a hardship was the medical expense. Whether the debt was already paid doesn't matter because it is the expense that is the hardship.
So, since costs related to the purchase of a primary residence is an eligible hardship under the safe harbor definition, does it matter that those costs first came out of the participants checking account if those costs could have been paid with the hardship distribution?
It will probably depend on the facts and circumstances, but I would not disqualify a participant just because they are looking to recover a payment they already made.