Why not? Who cares if they're actually standing? They can lay on the floor if you ask me, as long as they can share the status with team members.
I see a different problem with standup. Plenty of people applying the same rule over and over without understanding what's the real goal of standup. Plenty of people just take the virtual stick of the speaker (or sometimes not virtual) and say the same mantra every morning "I've done this, I'm doing that, no problems," and pass the stick to another.
But the real goal is not to check up on people to make sure they are doing something. In fact I couldn't care less if you are doing something or not. You could sit there watching cats videos all day as long as, in the end, all TASKS are completed. If you can sit doing nothing your team have a different problem, obviously, but that's another story.
The team have made a commitment on Monday that they deliver some features till Friday (assuming weekly iteration.) So what they do? They create tasks. The team is tracking the tasks on the board and the team should check all tasks every morning. Start with task #123. Who's doing it? John. So, John tell us about it - what's status, when can you complete, is everything smooth? Then you take next task - #124. Who is doing it? No one. But then John says he can complete current task today, so he's going to take it. And another task... Your standup should be about tasks, not about people. The difference is subtle, because it the end everyone should share the same info - progress, blockers, etc. But by checking on tasks the team members automatically build mental model of current iteration. How far are they? Is the tempo OK? Or maybe there's some delay and, finally, can they deliver on time? People will understand better where they are somewhere in the middle of the week and this is the key point. To share and understand. Not to report, forget and just go doing your job.
The output of the iteration is the work done. Check the work, not the people.