IMHO, just as your employer has an expectation for you to conduct yourselves professionally, there should be an expectation for employers to do the same, i.e. recognise that as adults we are entitled to our own space and privacy. That should be built into the budget for travel.
I work in a small, informal and close-knit team. I'm out at work and it is a complete non-issue - once when there was an event in Melbourne which I had organised and wanted to attend but couldn't get travel budget approved for, both guys and girls on the team offered to let me share rooms with them to help me out. (This still left the problem of getting there, and in the end I didn't want to go badly enough to spend my own points or $$$ on a work trip.)
What was interesting was the different reaction on another occasion when my manager had one of her periodic panics about budget and suggested on another team trip that we should share rooms in order to save some cash. This suggestion was greeted with a silence you could cut with a knife... at which point my manager realised it was none-too-popular, had a good laugh, and said she wouldn't suggest that again.
The point is, people were happy to offer to share in order to do me a favour, but were not at all happy with being forced to share. Although I could quite happily share a room with any of my team-mates (say, if we were going on a weekend trip somewhere) I would deeply resent being told I had to. Does that make sense?