Do you accept same day booking for a new dog?

I do accept same day bookings but I always require a Meet and Greet first. During our conversation, I will try to get as much information as possible. One question I found can really tell you a lot about the dog is asking the owner why they waiting until the last minute to find a dog sitter? (A lot of times their sitters canceled on them but other times you can find out about behavioral issues from this question.) I also specifically ask the owner if there are any medical or behavioral issues I should be aware of. As long as everything sounds good, and the pet(s) sound like pets I would normally take, I will schedule the Meet and Greet. I will be honest, I get a lot of push back on same day bookings about scheduling the Meet and Greet but I explain to the owner that the Meet and Greet is to make sure that not only are they comfortable with leaving their pet with me but also lets me evaluate their dog and make sure that my home would be a good fit for them. I will tell them specifically what I am looking for during the meet and greet. (example; if I need to make sure that their pet gets along with the pets I already have here, I will tell them that. Or if I want to make sure their pet is not going to mark all throughout the house I will let them know.) Basically I let them know what I am looking for that would keep me from saying yes when they get here. (If I already know that I am too full or have a dog that will not get along with their pet, I will not waste their time or mine.) 9 times out of 10, the Meet and Greets go well and they leave their pets. (while they are standing in front of me, I will approve their stay and make sure they approve it on their end before I let them leave their pet(s). )
Hope this helps. Best of Luck!

I do not board or offer daycare, so I imagine this situation may be different if you are allowing a dog into your home...but even for walking, drop-in, and house-sitting services, I require more notice and a meet and greet prior to booking. This is for my own sanity as I'm only doing this as a side job in addition to my full-time job and being a part-time student. It's also for safety purposes, as I want to make sure the person who is requesting my services is who they say they are and does not present immediate red flags.

I think you are well justified to decline as you did.