You can definitely get "rare" stuff in the normal gatcha. The girl even says "Hey, there's something rare. How about paying to see so you don't miss it", or something like that. (and fwiw, it may be less than a x in 3 chance (where x is number of rares) of getting the rare, but it is possible. They haven't rigged it to the point where it's impossible to get the rare unless you pay to look. Assuming furniture/clothing are all rares, their can even be multiple.)
That said, I don't *think* Momentos actually count as rares. I think the one I got was underwear. (the other options were dust, so I'm pretty sure what I got was the rare. I can't remember seeing furniture/clothing as a reward without getting the "something rare" message though.)