Given only one possible appointment for masters application interview with no possibility to renegotiate date: Is this a red flag or normal? Background:
I applied for several masters programs this season (taking into account the advice given on this site) and have received a request for a telephone/Skype interview with one of the German universities I applied for. The response came much more quickly than I expected and I still have no replies from other universities.

The mail contained suggested date and time (ten or so days from the date the mail was sent) and asked me to confirm it. Unfortunately, at the specified time, I'll be on a highway, in a different country, traveling between two cities. In my response, I explained that I'll be on a trip and that I'm coming back two days after the suggested date and that I'll be available pretty much at any time after I return from my trip. The reply I got is that the time suggested is the only available time for the interview.

Question: 
My unfortunate situation aside, I wanted to ask is it normal for universities to be this inflexible when scheduling admissions interviews? Did I go out if line by attempting to negotiate the interview date? This is the first time I'm having any sort of interview, so I really have no idea what are the cultural norms in such case.
I think it was perfectly reasonable of you to ask to reschedule.  Of course, it's unfortunate that they weren't able or willing to accommodate you, but that's up to them.

You'll now have to decide what you want to do: interview while traveling, or alter your travel plans, or skip the interview altogether.  It might be worth considering whether an institution that seems so unwilling to accommodate prospective students is an institution that you'd want to attend at all!