Wealth tax is irrelevant for debt repayment. If they keep the loan, their gross wealth is higher (as the loan will be e.g. on a bank account or invested somewhere) but they can deduct the loan value as debt. The net worth remains the same in any case, assuming no tax evasion.
I agree that the claimed effect on (income) taxes sounds wrong. It would imply a marginal income tax rate above 100% which is not possible in Switzerland. That’s assuming you don’t hit a special case such as being able to get health insurance discount due to a low taxable income but that’s normally not even visible in the tax assessment, and I don’t know whether debt interest deductions are even relevant for that.