One of my pages uses the archive.php template only. Why?

When you use pretty permalinks, WordPress creates a set of rules for each type of content. These rules define a pattern that each type of content’s URL’s will follow.

When you have an incoming request, WordPress decides what is being requested by matching the URL with these rules. If multiple rules match, the one with the highest precedence is used. In this case, your CPT takes precedence over pages.

See the WP_Rewrite class in Codex for more info.

EDIT Also see parse_request in source for the code that parses these rules for a request.