I am from San Francisco, and I re-read the comments from the original article to discover what restaurant this was. I am familiar with this restaurant (actually it's a brewpub) and just knowing that, I would be willing to bet money that the restaurant was indeed the rudest one here.
This place is a pretentious hipster's paradise, to put it bluntly. First of all, to answer a question that many have mentioned, this place does NOT take reservations. This is a new trendy thing many restaurants are doing here to create a "buzz". Somehow, it makes your place seem cool and exclusive to have people lining up before the place opens hoping to get a table, and to have throngs of people waiting on the sidewalk outside.
Also, the restaurant is in a converted warehouse, so actually a pretty large space and not your typical urban small bistro. However, much of the dining area is taken up by long communal tables, as well as a lot of high bar tables with stools...neither of which would work well with a stroller, or even a high chair for that matter.
I can totally imagine a group with a stroller choosing this restaurant because it seems like a big open space, only to become flustered when looking inside to find that there was really only one table where the stroller would be feasible. I can also imagine waiting a full 35 minutes for a specific table.
Because they don't even take reservations, having someone come in after you and get seated at the table you had specifically requested is basically a slap in the face. My bet is that they (the restaurant) were hoping the OP's party would leave if the wait was too long. And when they didn't leave, they sat them at a table that they knew was unacceptable. Then they claimed that the party they asked to switch was "irritated" so they could ask them to leave.
The only thing the OP's party did that could be construed as wrong was to ask to switch tables. However, if they asked politely and the other party agreed to switch, I can't really fault them. For those who think just asking to switch is rude in the first place, do you also think it is rude to ask someone to switch seats on an airplane? It just seems to me to be easier to ask the person directly (accepting a no answer gracefully, of course) than to try to get the flight attendant to ask them. In the restaurant situation above, they were getting attitude from the restaurant staff and thought asking directly would be a better way.