I can see how a coworker would think it's their business because it's easy for this sort of thing to creep until *everybody* feels like they are under pressure to skip a funeral for a minor work thing. I am constantly telling coworkers to take off for whatever and we will make do, because being loud about that is the only way to keep down *my* guilt over skipping out on them for any reason, and also a lot of staff *do* feel like they need to skip important life things for work (they don't). If coworker kept pushing after LW explained that she didn't feel pressured to skip the funeral, that coworker is being pushy and awful, but I can't tell if they did.

On the other hand this is absolutely not coworker's business.

I would probably have gone with something like, "Oh, no worries, the work event is just a convenient excuse to not have to go, the family situation is complicated!" and then refused to continue on that topic. But that's not going to work for everyone.