I think White is missing the meaning of 1 Cor 3:14-15. Here are a bucket-load of translations:
(RSV) If the work which any man has built on the foundation survives, he will receive a reward. / If any man’s work is burned up, he will suffer loss, though he himself will be saved, but only as through fire.
(NAB) If the work stands that someone built upon the foundation, that person will receive a wage. / But if someone’s work is burned up, that one will suffer loss; the person will be saved, but only as through fire.
(KJV) If any man’s work abide which he hath built thereupon, he shall receive a reward. / If any man’s work shall be burned, he shall suffer loss: but he himself shall be saved; yet so as by fire.
(DR) If any man’s work abide, which he hath built thereupon, he shall receive a reward. / If any man’s work burn, he shall suffer loss; but he himself shall be saved, yet so as by fire.
(LV) si cuius opus manserit quod superaedificavit mercedem accipiet / si cuius opus arserit detrimentum patietur ipse autem salvus erit sic tamen quasi per ignem
(BNV) Si cuius opus manserit, quod superaedificavit, mercedem accipiet; / si cuius opus arserit, detrimentum patietur, ipse autem salvus erit, sic tamen quasi per ignem.
Where is the confusion? All who go through the “fire” of purgatory are cleansed and are saved, and thus rewarded, whether their works perish or not. The Greek word is sozo, which Strong’s indicates is never translated as “preserved”, so Paul did not mean that the fire would destroy the works but preserve the person, so as to receive Hell or Heaven. Paul meant that the person would be saved – that is, receive final salvation.