I think the issue is you dont have 'iframe' as an "allowed HTML tags" for the profile that that user is in.
Go to:
ACP -> CORE -> SYSTEM CORE -> QUOTA CONFIG -> allowed HTML tags
and add ',iframe' to the list of allowed html tags so it looks something like this:
span,strong,em,a,b,u,i,p,div,br,img,h1,h2,h3,h4,pre,hr,ul,ol,li,sub,sup,table,tbody,th,tr,td,div.style,iframe
The logged in users being able to see it would be the owner of the profile and the admin user.
The owner of the profile can see their own things.
The admin user can see everything.
I think this is what is happening, if you can still sett the issue after adding 'iframe' then I'll need specific steps to setup to investigate further.