That was my understanding as well, but I found this halacha in the Shulchan Aruch and in the Mishnah Berura, -a translation is included-:
שולחן ערוף סימן קיג
ח המתפלל ובא כנגדו י אדם ויש לו תמונת עבודת כוכבים (יד) בידו והגיע למקום ששוחין בו לא ישחה (טו) אע"פ שלבו לשמים:
משנה ברורה סימן קיג
ח (יד) בידו. עיין במ"א במה שכתב דאם הוא וכו' אבל במגן גבורים כתב שחלילה להקל בזה ובפרט בעת התפלה:
(טו) אע"פ וכו'. מפני שנראה כמשתחוה לעבודת כוכבים:
Shulchan Aruch Siman 113 Seif 8
If while one is praying a person who has an image of an idol in his hand comes in front of him, then, if he has reached the stage where one must bend forward he should not bend forward, although he has in mind that he is bowing to Heaven when he bends.
Mishna Berura Siman 113
In hand. See what the M.A. writes that if he, etc. However, the Magen Giborim writes that /God/ forbid that one should be lenient about this, especially when he is praying.
Although, etc . For he will appear to be bowing to the idol.
Siman 113 deals with the laws of bowing during the Amidah that happens to be the core of praying, so probably in a hospital, where there may not be other venue, there may or may be not some leniency.
As for praying, if one's back is to the cross and you are four amot away, I don't see why it would be different that any other objectionable object. One would not bow during the prayer since one has to be careful not to bow at anytime in the room. To this we can add, that the crosses are not there for prayer but as a decoration similar to the suppostition that most non-jews are wearing the cross as a decoration and not as an object of worship.
As I said, in a church you can't bow and you should be careful not even to bow incidently. As for visiting churches for their historical or artistic content, if it is no longer used as church some permit. Nobody permits going into a functioning church for this reason but a lot of people ignore this. Personally I skip the churches in general but I wouldn't want to pass up on the Mabda map.