"...before he blabs to another dog or one of those pesky squirrels that have been nosing about. They're on Vickie Vale's payroll, I just know it!"
Y'know Bats, he's been hanging out with Bruce and Dick too.
Hmmm. Let's look at this closer: While a dog's brain is only one-tenth the size of a human brain, the part that controls smell is 40 times larger than in humans. A dogs sense of smell is about 1,000 to 10,000,000 times more sensitive than a humans (depending on the breed). A human has about 5 million scent glands, as compared to a dog who has anywhere from 125 million to 300 million.
So, what'dya think: you'd put your masks on and he'd freak out wondering where you went? Like an infant in a game of peek-a-boo?
He's obviously allowed access to Wayne manor in order to get the pic. Heck, he could've just wiped his butt on the Bat-Floor and it stuck.
This is why Silver Age Batman is so cool. It's not aimed at adults but neither is it aimed at sanity.
I kid because I love!