There is Roth Conversion and there is recharacterization.  Conversion is taxable to the extent the rollover does not represent a return of basis - this is the back-door IRA, at least for individuals who would not otherwise qualify because of their MAGI.  Just about the only times when a conversion is not taxable is (1) the taxpayer has no other IRA, opened a brand new IRA, and rolled over everything (likely immediately) without any gain/loss or (2) the taxpayer rolled over all pre-tax dollars to a 401(k) and converted what's left in the IRA to a Roth.

Recharacterization from a traditional IRA to a Roth is not taxable but the taxpayer would have to be eligible for Roth contribution in the first place.  This is not a back-door IRA.

Based on the above, which one fits your client's fact pattern?