Question

 
When the Talmud presents a tzrichuta in order to explain two cases where the guiding principle behind their ruling is repeated, do both sides of the tzrichuta have to be able to hold true?
 For example: suppose the Mishnah had been formulated as follows: One must separate tithes from a pear; one must separate tithes from an apple. The principle being repeated here (all this hypothetically) is that one must separate tithes from fruit. It would make sense according to the rule I presented above if the Talmud were to explain that the two fruits are different, and that their characteristics include different halakhic definitions that do not overlap—in this case, the apple has halakhic definition X, which does not apply to the pear, and the pear has halakhic definition Y, which does not apply to the apple. Those halakhic definitions (X and Y) would have led us to think that both the apple and the pear were exempt from tithes, and so the Mishnah comes to teach that fruits included in definition X are obligated in tithes, and fruits included in definition Y are also obligated in tithes.
My question is: is it correct to say that the rule I tried to present and illustrate is not necessary? I’ll give an example of what I mean. The Mishnah in tractate Sanhedrin, chapter 3 (brought in the Babylonian Talmud, Sanhedrin 24b), mentions pigeon-flyers as a type of people who engage in an activity that disqualifies them from giving testimony. The Talmud there (25a–b) tries to clarify the term pigeon-flyers. One of the opinions explains the term as a kind of gambling game, a competition between pigeons in which the winner is the one whose pigeon reaches the target first [a game still common today, mainly in East Asia]. The Talmud then asks: after all, earlier in our Mishnah we already learned dice-player; so why did the Mishnah teach two identical disqualifications in the same Mishnah? Then it presents a tzrichuta for the two rulings. It assumes that the dice-player relies on his own judgment, whereas the pigeon-flyer relies on his pigeon’s judgment (in the language of the Talmud):
 (I’m writing all this in a somewhat paternalistic style so we don’t get bogged down in an example that isn’t the main point.)
“It is necessary—for if it had taught one who relies on his own judgment, there it is that he does not fully resolve to transfer ownership, because he says: ‘I know within myself that I know better.’ But in the case of one who relies on his pigeon, say no. And if it had taught one who relies on his pigeon, there he says: ‘The matter depends on the knocking, and I know better how to knock.’ But one who relies on his own judgment, say no—therefore it is necessary.”
 In short, in each of the cases (relying on his own judgment, and relying on his pigeon’s judgment), I would have had an initial assumption that the person does not fully transfer ownership willingly, because he thinks there is some factor dependent on him that can, in his eyes, guarantee his victory. Therefore the Mishnah taught both, so that I know that in both cases they are disqualified from testimony. But here the observer is faced with a question: the Talmud assumes that it was impossible to teach only the first case or only the second case, because in whichever case I would have learned, I would have thought and projected onto the other case that it is random, and therefore there is full intent in the transaction, and so that person would not be disqualified from testimony. But the two initial assumptions cannot both exist together—if I think that in the case of relying on his pigeon’s judgment there is no full intent in the transaction, then in my view in the case of relying on his own judgment there is full intent in the transaction, and vice versa.
All of this is unlike the example we gave of the apple and pear, where the assumption that halakhic definition X applies to the apple does not at all contradict the thought that halakhic definition Y does or does not apply to the pear. In short: there are tzrichuta cases where what is learned about the first case has nothing to do with the second case (the apple and the pear), and there are ones where they teach one thing and its opposite (relying on his own judgment and on his pigeon)—if I were standing at the vantage point of the first case, I would think the second does not apply, and vice versa.
I’d be glad to know what the Rabbi thinks. Is this a correct distinction, or a foolish one, or perhaps something in between?