Horn speakers are really bright?

Hard to comment judging with computer speakers of course, but no, it doesn't sound bright, but full disclosure, I use Epic CF 4 speakers as well, and no, they're not bright. I think the demo music wasn't ideal as it was very wispery.
By the way, that's the best garage system I ever saw!

I don't find most horn systems to be "bright" (pronounced top end response), but, many do have a peak in the upper midrange that some might consider "bright" in sound.  The very best horns don't have that kind of peak, but, few have heard the best compression drivers on the appropriate horn (e.g., Western Electric, IPC, G.I.P., YL, Raycon drivers and horns).

Another issue is the appropriate amplifier.  Horn drivers are extremely detailed and revealing of different amplifiers being used.  It is very important to find the right amplifier match (typically low and medium powered tube amps).  The wrong amp can sound thin or harsh and "artificial."  While I am not a Klipsch fan, I think the classic speaker line is quite decent sounding when they are coupled to the right amplifiers; most often they are heard at dealers being run with crappy electronics so I can see why there are a lot of people who do not like the sound of horn systems.

Dig Sophie Zelmani. Garage sounds better! I don't get the "too bright" thing either. Unless it's searing your ears off, or just plain messed up frequency response,  you can't have enough detail.

Garage sounds good, very open and revealing. KLF in living room sound very bright to me. Voice not bad, but guitar and instruments sound thin with so much high-end energy.
BTW, I can hear up to 18kHz and I think the iPhone is positioned too close to speakers.