The Gemara (Gittin 81b) learns that according to Beis Hillel, witnesses on the seclusion are like witnesses of the actual action. That is, watching the couple walk into a room together is enough for Kiddushin.
The Rambam (Ishus 3:5) writes as follows:
וְאִם קִדֵּשׁ בְּבִיאָה אוֹמֵר לָהּ הֲרֵי אַתְּ מְקֻדֶּשֶׁת לִי אוֹ הֲרֵי אַתְּ מְאֹרֶסֶת לִי אוֹ הֲרֵי אַתְּ לִי לְאִשָּׁה בִּבְעִילָה זוֹ וְכָל כַּיּוֹצֵא בָּזֶה. וּמִתְיַחֵד עִמָּהּ בִּפְנֵי שְׁנֵי עֵדִים וּבוֹעֲלָהּ.
If he does Kiddushin with intercourse, he says to her, “You are Mekudeshes to me,” or “You are Me’oreses to me,” or “You are to me a wife with this intercourse,” or the like, and he secludes himself with her before two witnesses and has intercourse with her.
Picking up on the fact that the Rambam only mentions the witnesses in connection with the seclusion and not the intercourse, the Maggid Mishnah writes:
בגיטין פרק הזורק (דף פ"א) אמרינן הן הן עידי יחוד הן הן עידי ביאה ופשוט הוא שכל האומר שעל דעת לקדשה מתייחד עמה והוא בפני עדים הן הן עידי ביאה:
In Gittin in Perek HaZoreik (daf 81) we say “These are the witnesses of seclusion - they are the witnesses of intercourse.” It’s obvious that anyone who says that with the intent to marry her he is secluding himself with her, and that is in front of witnesses, that they are the witnesses for intercourse.
But if the witnesses don’t actually see the intercourse, how can we be certain that it actually happened? In short, we can’t.
The case Beis Shammai and Beis Hillel we’re discussing is when a man gives his wife a get and then is intimate with his wife. Does he need to give a new get? Beis Shammai for once is lenient, and Beis Hillel stringent. In the conclusion of the Gemara, the case is that there were Eidi Yichud but no Eidi Bi’ah.
Rashi explains the reason behind Beis Hillel’s opinion that Eidi Yichud are considered like Eidi Bi’ah:
הן הן כו' - כלומר כיון דראו שנתייחדו אין צריך עדות של ביאה גדול מזה ודאי אנן סהדי כיון דגייסי אהדדי לא פרשו זה מזה:
Since we see that they are secluded, we don’t need a greater testimony to their intimacy than this; we are witnesses that since they are close with one another, they won’t separate from each other.
In other words, once he says he’s going to be intimate, we assume that he is. You’re correct - maybe something will prevent them from acting. But we act on the chazakah of לבו גס בה.
This logic of לבו גס בה applies in the other direction also - in a case where they were divorced only after Kiddushin but not Nisuin, the Gemara rules that even Beis Hillel won’t require a second get:
ומודים בנתגרשה מן האירוסין שאינה צריכה הימנו גט שני דכיון דאין לבו גס בה לא אמרינן הן הן עדי ביאה
They agree when they were divorced from Kiddushin that she doesn’t need a second get, for since he is not close with her, we don’t say that they are witnesses to the intimacy.
This lack of absolute knowledge isn't a problem here. Witnesses for Kiddushin are not there, as you say, to verify if Kiddushin occurred. It's not like if there weren't witnesses they'd be married and just unable to convince anyone else of it. Having witnesses is part of the ceremony itself and here their being just outside with a presumption of intent and action is sufficient to make the ceremony effective. If there is actually a doubt if marital relations are occurring in a marriage (eg. one spouse sues the other for divorce with this claim), then witnesses of seclusion are insufficient and the court can't adjudicate the case further (Rambam Ishus 14:16). It is prohibited to bring the witnesses into the room itself to observe due to modesty concerns (ibid.). Indeed even effecting Kiddushin with the witnesses outside the room is strongly discouraged and one is lashed for doing so (ibid. 3:21).
In summary: Witnesses to the seclusion are enough for Kiddushin to be effective. Since he says he’s going to be intimate with her and we see that they are close with one another, we trust the presumption and declare it an act of Kiddushin. There is no way to really verify if intercourse actually took place, but that is not a problem for Kiddushin.
