You're correct that your DNS queries and answers can set the case bit, but the protocol design always said that while the answers must match the query, the case isn't actually significant. For a long time that's just an obscure Um Actually nerd trivia question, but traditional (before DPRIVE) DNS is very old and is mostly a UDP protocol, so people try to spoof it, let's follow that story:

At first: The only anti-spoof defence provided in DNS is an ID number, initially people are like 1, 2, 3, 4, 5... and so the attacker watches you use these IDs then makes you ask a question, "6: A? mybank.example" and simultaneously they answer "6: A 10.20.30.40" before your real DNS server could likely respond - choosing their own IP address. Six is the expected ID, you just got spoofed and will visit their fake bank.

So then: DNS clients get smarter using randomisation for the ID, 23493, 45390, 18301... this helps considerably, but bandwidth is cheap and those IDs are only 16-bit so a bad guy can actually send you 65536 answers and get a 100% success rate with spoofing, or more realistically maybe they send 1000 answers and still have more than 1% success.

Today as a further improvement, we use Paul Vixie's bit 0x20 hack which uses every letter of a DNS label to hide one bit of entropy in the case in addition to the random ID. Now the attacker has to try not only different IDs but different case spellings, A? mYbANk.eXAmpLE or maybe A? MyBANk.EXAMple or A? mybaNK.EXamPLE -- only responses with the right case match, the others are ignored.

So, because of all this security shenanigans, your DNS client knows that case in DNS queries doesn't matter and will do what we want for this purpose.

[Edited: fixed a few typos]