Well, as you said, it does fall apart when you think it through. That's exactly what happened in the third part when Superman wondered where his indestructible costume came from, about Krypto, and why Supergirl kept calling him 'cousin' when his mutant origin story meant they weren't related at all.
But the thing that I thought they were going for to explain these inconsistencies was an older concept Maggin (?) introduced about his super-power of suggestion. Luthor once took advantage of this to make Superman believe he had the power to turn him back into Superboy with a gadget when he apparently did so to Batman and the Flash. Ordinary people can be hypnotized into believing something has happened that didn't. Superman's mind is so powerful that whatever he believes is made into reality. So, if he believed he could be turned into Superboy, then he turned into Superboy in fact. By refusing to accept this reality anymore, he returned to being Superman and beat Luthor soundly.
The super-hypnotism was used as a way to explain why if people having pictures of Suerman and Clark Kent side by side could not spot the simularities. Seemed Superman created a Super-hypnotism effect when wearing his Clark Kent glasses that was so powerful that it extended to photos.
On a side note I vaguely remember a story where Superman is trying to reveal his secret id and this kid will not believe him. While not mentioned the plot device of the Super-hypnotism come up when trying to convince the kid he is Superman Lois runs in and open up his shirt to reveal Superman's costume. At which point she berates Clark Kent for pretending to be Superman!
At wits end Superman asks what will prove that he is Clark Kent and the kid askes of all things to see Kent's bathroom. He opens up the medicine cabinet and finding it empty say now believes because Superman would not need things a normal man would have in his medicine cabinet like shaving cream, razor, medicine for the occational illness and so on. I think the kid wad related to Pete Ross but it has been so long I'm not sure.