I wouldn't use this site, no. First of all, it's not difficult to find out who owns rights to the music you want to use. Often it's as simple as heading over to Amazon Music and looking at the record label that put out the album. They're trying to make it seem like they're giving you some "premium" service of direct contact info, but I doubt it's anything worth paying for.
I'd use Harry Fox. Harry Fox tells you exactly who owns the rights to the song just by searching their directory. Furthermore, you don't "hire" Harry Fox to go out and get rights for you... You just add them to your cart for a fee, that usually isn't too large.
This Clearance website just looks like it's trying to bully and scare-tactic people into buying their services - Thus having pictures of skulls, bars, jail, and whatnot all over their website on pages like "HORROR STORIES!!"
Avoid it. Just go get your rights with Harry Fox, or contact the rights owner on your own by doing some research.
Oh, and another thing... The whole "Click on the page titled 'Fees' so we can divert you to contacting us instead of posting our fees' is a cop-out to try to capitalize on people not understanding the industry. And I'm sure it helps they furnished the page like Shawshank Prison.