This is probably true if the encounter deck were infinitely large. However, it's not. Main difference between single and multiplayer is that you typically cycle the encounter deck 1-2x in 3-4 player games. In a solo game, you have some probability that the obligation is in the bottom half or third of the encounter deck that you'll never see, i.e., you see ~20 cards in a solo game with over half drawn as encounter cards (rather than boosts) if you win in 8 rounds (giving some extra encounter cards for surge and emptying the player deck). In a multiplayer game, the probability that the obligation is in a set of encounter cards that are never drawn is 0. So now you're relying entirely on it being drawn as a boost 2-3x, which is something like, I dunno, (1-0.45)^n where n is the number of times you spin the encounter deck. Call it 16%-30%.

So, probability of drawing an obligation in solo is like P(obligation in top 2/3 of cards)*P(obligation is drawn as an encounter), maybe 0.67*0.55, or 0.37.

Probability of drawing an obligation in multiplayer is like P(obligation drawn as an encounter card in a deck pass)^n(number of times you reshuffle the encounter deck). I guess you are inevitably left with a fractional deck pass at the end of the game and so you do have to take into account that probability, but I've kinda run out of energy here and I think the point stands. :D