We have probably exhausted the potential for worthwhile debate on the topic, especially given our very different readings of that paragraph in the DMG. But thank you! It was a fun discussion.
Indeed. I'll leave you with this which gives an example of what the DMG is talking about in that section (page 239, for anyone who wants to see what [MENTION=467]Reynard[/MENTION] was referencing). So here, from Basic Rules, page 2:
Dungeon Master (DM): OK, one at a time. Phillip, you’re looking at the gargoyles?
Phillip: Yeah. Is there any hint they might be creatures and not decorations?
DM: Make an Intelligence check. <---
Phillip: Does my Investigation skill apply? <---
Phillip (rolling a d20): Ugh. Seven.
DM: They look like decorations to you. And Amy, Riva is checking out the drawbridge?
In other words, "Often, players ask whether they can apply a skill proficiency to an ability check."