Even in places where the two rabbis in the previous Mishnah said that you were allowed to rent houses to idol worshippers, that was according to Rebbe Meir anywhere outside of Eretz Yisrael (Israel), including Syria. According to Rebbe Yose, even in Eretz Yisrael you were allowed to rent a house to an oved kochavim (idol worshipper).
When they allowed renting to an idol worshipper, we did not say that you were allowed to rent them a house where they would be able to live. If they were able to live there, an idol worshipper would bring idols into the house he rented. And that house really belongs to a Jew. You are not allowed to have an idol brought into your house. As the pasuk (verse) tells us, you are not allowed to bring an abomination, meaning an idol, into your house. So when we said that you are allowed to rent houses to an idol worshipper, we were not talking about living there. What we really meant was using the house for storage, where people are not going to bring an idol in with them.
Now that we have brought that up, we will bring up a similar issue. On Shabbat, a person who is profit-sharing with an idol worshipper is allowed to have the non-Jew work, even on Shabbat, and they will share the profits, because it is known that it is be'arisut; it is known that there is a partnership going on between them. But in certain types of businesses, where it is obvious that there is no partnership between the goy (non-Jew) and the Jew, but the goy is paid a certain salary that stays the same no matter what profit is made, it would be an issue for a Jew to hire that goy on Shabbat. It is very obvious that the Jew is the one making the profits and that the goy is working for the Jew on Shabbat.
So if a Jew rented even a bathhouse to an idol worshipper, he rented the whole thing to him. Technically, the idol worshipper is not working for him. It is his own place; he rented it and is doing what he wants with it. Therefore, this prohibition would not apply. But the rabbis said that you are not allowed to rent a bathhouse to an idol worshipper anyway. In all situations, whether you are in Israel or elsewhere, it has nothing to do with the location. You are not allowed to rent the bathhouse to an idol worshipper because the bathhouse is called by the owner’s name, by the Jewish owner’s name. Even if he rented it out, people are going to know it as this person’s bathhouse. They are talking about the owner, the Jew.
So when an idol worshipper is watering or heating up water on Shabbat, people are not going to think that he rented the bathhouse, even though he really did. They are going to think that, the way a bathhouse works, there is no be'arisut, no partnership. The way it is working, if the Jew is the owner and the non-Jew here is working for him. So they are going to think that the goy is doing work for the Jew on Shabbat, and that would be a halachic violation. Even though that is not true, because the goy rented the whole bathhouse and the Jew was just collecting his rent, it is still a problem because of the mar'it ayin (appearance of impropriety) issue: that is how it usually works. There is no concept of partnership when it comes to a bathhouse, so people could assume that the goy is working for the Jew. Therefore, we say that you are not even allowed to rent the bathhouse to a goy in any situation, because of how it would look.