Query question: who is this?

I just got a rejection that took me aback. It was a typical form rejection (other than one rather brusque line), thanking me for approaching the agency, but the query didn't hook them. 

However the person who responded to my email wasn't the agent I queried, but an intern as identified by their signature. I've received rejections from assistants or interns before, but always on behalf of the agent or at least the agency. This response was all I statements, as in "I am frequently overwhelmed with commitments to my current clients, so in any given year I must be selective taking on any new author."

The email was signed by the intern and came from their account, no mention of the agent at all.

(1) Is this common?
(2) Do interns get their own clients
(3) Is this a red flag that the agency isn't very professional,  or
(4) am I being overly sensitive and savoring my sour grapes?

Let's go in reverse order:

(4) No you're not being overly sensitive. It's not asking too much to have the person to whom you directed your correspondence either reply herself OR direct a person to reply on her behalf. For The Correct Way to Attend to One's Correspondence it's hard to beat the example set by Her Majesty the Q, and here's how those letters from her interns ladies-in-waiting are worded:

"The Queen wishes me to write and thank you for the matched set of unicorns you have sent on the occasion of her Golden Jubilee. etc."  

You'll notice the letter writer makes it clear it is not The Q herself writing the letter.

(3) No, it's a sign the agency has farmed out their queries to interns without much supervision.

(2) No.

(1) No.

If an agency is not supervising their interns, or is ok with interns writing directly instead of on behalf of the agent, they deserve what comes from that: you think less of them. I do too.