Your professor is an idiot. There is no reason that the rest of the group should be punished for one person's slackassery.
Conversely, I've always found it annoying when people whine about the unfairness of their grade being affected by their team members. Tell the teacher about problem team members certainly, but the time to deal with problems is BEFORE the project is due, not after; be proactive, don't be a whiner.
Sorry folks, in the real world you gotta deal with other people's shit, so in your group projects you are learning (among other things) how to deal with other people's shit. You are a team, and you get graded as a team. I mean, if the performance of other people in your group shouldn't affect your grade, then why even do a group project? Why not simply have each person turn in their own paper?
I remember once when she was studying for her MBA, my fiancee went on a rant one night about how one person in her group was a slacker and not doing their share of the work, and the project was due on Monday (it was the weekend.) I nodded along, sympathizing, because I've certainly been there and it is extremely frustrating. When she was done ranting she took a deep breath and asked, "So what should I do?" I responded, "Well, you should do the work." I mean, in the long term you want to avoid working with the slacker again, and probably communicate that fact to the teacher, but in the short term you have a paper to do.
Again, think of the real-world: If you have to work together with other people in your department to prepare a report for the board or something, then if the report sucks you all get chewed out. Whine all you want about whether or not it's fair, but that's how it is, so learn to deal with it. The time to complain to your manager about slackers on the team is as soon as the problem is apparent, not after the board has seen the finished report.
What I wish is not that teachers were more "fair" in grading group members, but that more teachers were explicit about the point of group projects. That is, they directly state up-front that because group projects are for you to learn to work in a group, your grade is in part a reflection of how well your group functions.
I also wish teachers taught a bit more directly how to function in groups rather than simply expect people to figure it out on their own, but then it's mostly common sense sort of stuff that people just seem to forget.
On a closely related note, people also whine about it being unfair if they can't choose their own group members. There are compelling arguments both ways, but personally I prefer randomly-formed groups for group projects in classes. This is a view I've had crystallized from classes I've taken but note that I haven't enforced this in any classes that I've taught. I have a couple anecdotes to share about this too, but I don't really want to rant here too much (at least not right now, heh.)