it's not a troll but it's a shitty explanation
the key point in that little riddle is that the interviewer knows which envelope contains the acceptance letter, and that he will not reveal the acceptance letter when he shows you that one envelope
in a standard situation, you have three pairs of outcomes, six total:
1. you select acceptance letter, he reveals rejection letter #1
2. you select acceptance letter, he reveals rejection letter #2
3. you select rejection letter #1, he reveals rejection letter #2
4. you select rejection letter #1, he reveals acceptance letter
5. you select rejection letter #2, he reveals rejection letter #1
6. you select rejection letter #2, he reveals acceptance letter
given the assumption that he has perfect information, outcome #4 and outcome #6 will not happen. however, if he does not know what envelope contains what, and there is a chance he will reveal the acceptance letter, then this question is moot and switching makes no difference. the perfect information assumption is key.
so you have outcomes
1. you select acceptance letter, he reveals rejection letter #1
2. you select acceptance letter, he reveals rejection letter #2
3. you select rejection letter #1, he reveals rejection letter #2
5. you select rejection letter #2, he reveals rejection letter #1
if you select an acceptance letter, there is a 50% chance he will reveal one of the rejection letters. which one is irrelevant. so outcomes 1 and 2 can be condensed into one result.
if you select a rejection letter, he has no choice but to reveal the other rejection letter.
so there are 3 possibilities with equal probability:
(1) you select acceptance letter, he reveals either rejection letter with 50/50 probability
(2) you select rejection letter #1, he reveals rejection letter #2
(3) you select rejection letter #2, he reveals rejection letter #1
(1) - switching LOSES
(2) - switching WINS
(3) - switching WINS
kmz had the right idea but phrased the question wrong and explained it incorrectly