No, everyone has a feedable pet because of this event. This quest is after you have completed the five that award the Owl. So all people have to do is claim the Owl, put it out, and feed it. This same misunderstanding happened on the Beta forum too.
EDIT: I originally posted this to explain that the owl was given as a reward for completing 5 quests, but that's unnecessary now as you explained above!
For what it's worth, I don't collect these buildings right away either, intentionally. I wait until I get into the next chapter, then collect -- that way they're 1 chapter higher and you don't need to use RR spells to get them there.
Too often I'm in a hurry to spend and usually currency mismanagement occurs. With this event, I was determined to do things differently. I was going to gather keys and not spend for quite awhile. I used them to make an attempt on the daily (which I obtained) and then put them away for the next daily pursuit because the path will be there.
Thinking more about it now, I received the base from the quest box, not post office (so irrelevant for key spending), but didn't register as an option at quest nine because I was already ignoring it for later. I was fixated on quests and not prizes (unless they were time sensitive).
Brain glitch? 2+2=what?!?
Ugh Looks like one of those days... *sigh*
I have heard about waiting to claim if on the edge of chapters, but I don't recall it an option. It was, "here you go, its yours, bye."
If someone sees this early enough, I'd love to see a pic for how to delay that redemption.