IMO you are not being unreasonable, especially in this employment market. I have recruited many people and I would not have a problem with this. I do ask if people are attending other interviews, and as long as you did not lie to me then I would not have a problem. I only want people to join my employer if they really want to. Changing jobs is a big decision and I want them to be motivated to join my employer for the right reasons, if they have found a better job in the interim then so be, it is supposed to be a free market.
As long as you let them know asap i.e when you know the outcome of your other interviewing. Also people sometimes accept a role and then change their mind.
In this market you need to keep options open, I was speaking to a recruiter who was saying that employers are often making offers and then withdrawing them, not something I have ever had to do (unless it was because of poor references for example). Although, I presume the offer that you have accepted is subject to the usual - i.e. contract, satisfactory references and any other vetting, or medical info they might have in place.
Also if someone joined and did not work out many employers would have no problem invoking a probation clause whereby you are given a weeks notice (this is also discussed at interview). A good recruiter should try have your motivation for moving in mind, so that the placement is a win win situation for both parties. Good Luck!
Also I always either wrote or contacted the back up candidates and let them know where we were at so that I could go back and offer the role to the runner up if required. As soon as you have made your decision let them know though.
sorry for such a long post I could go on and on.