A logo can be as simple or as complex as a good logo designer can create.
I don't think the logo you envision is out of the question. It kinda depends on what you plan to use it for. Will it only be for your web site? If so, then you may be thinking of something more like a masthead. Which would be the top part of your site. Lots of church sites use that area for different graphical themes. This is common for sites designed for Wordpress. It's just a part of the site that takes the top portion of usually the home page (or all pages) and can have a nice graphic element representing the theme or feel of the site.
Most logos are designed to be flat, versatile and vector based, especially when used for printing, like on business cards, t-shirts, paper stock, coffee cups, etc. Which is why they are usually very simple. If you just want your logo on your site then it can be any way you want. You'll run into trouble later on if you want to put it on business cards.
When I think of complex logos, I think of movie company logos like Paramount, 20th Century Fox, DreamWorks, MGM and even Disney. When seen on the tv/movie screen they are usually pretty detailed and portray a vastness about them. But there are versions of the same logos made small enough to be put on stationary and still be recognizable -- just most of the detail is left out. For example, the DreamWorks logo is a boy sitting on the crescent moon with his fishing rod surrounded by clouds. The smaller versions are just the boy on the moon with the fishing rod usually in black and white and no detail, like a silhouette. Sometimes just the name of the company -- DreamWorks.
If the artist can also make a silhouette version of your logo, then it is definitely doable.
I think the person you talked to may just be thinking from a branding perspective and wants to stick with the rules of logo creation they were taught.