The standard formulation of the problem is such you are the one making the bizarre contortions of conditional probabilities by asking a question. The standard setup has no children with the person you meet, he tells you only that he has two children, and you ask him a question rather than them revealing information. When you ask "Is at least one a boy?", you set up the situation such that the conditional probabilities of various responses are very different.

In this new experimental setup (which is in very real fact a different problem from either of the ones you posed), we end up with the following situation:

h1 = "Boy then Girl"
h2 = "Girl then Boy"
h3 = "Girl then Girl"
h4 = "Boy then Boy"
o = "The man says yes to your question"

With a different set of conditional probabilities:

P(o | h1) = 1.0
P(o | h2) = 1.0
P(o | h3) = 0.0
P(o | h4) = 1.0

And it's relatively clear just from the conditional probabilities why we should expect to get an answer of 1/3 in this case now (because there are three hypotheses consistent with the observation and they all predict it to be equally likely).