I did. They say it is the index.php that is doing that.
Here's the dialogue with the support:
[07:50:21] Andrew P: It's your index.php file doing that
[07:50:40] Fernando: how can one tell?
[07:50:54] Andrew P: When I disabled it the site directory loaded fine without redirecting.
[07:51:25] Fernando: Sorry. Disable what?
[07:51:27] Fernando: how?
[07:52:06] Andrew P: I moved your index.php to index.php.off
[07:52:12] Andrew P: Then tested the site, and it was no longer redirecting
[07:52:17] Fernando: WOuld you say that page got corrupetd?
[07:52:19] Andrew P: That's how I know it's something in the code of the site causing this
[07:52:21] Andrew P: I'm not sure
[07:52:40] Fernando: does the site work without index.php?
[07:52:52] Andrew P: It loads the directory listing
[07:53:03] Andrew P: Maybe replace it with a default Joomla index page? Not sure.