Never Suicide and The Coroner Doth Protest Too Much

The pages for Never Suicide and The Coroner Doth Protest Too Much seem to imply that they're mutually exclusive. But what if the killer tries to make it look like a suicide and carelessly leaves behind some evidence, which the coroner then dismisses/ignores? Is that an example of both or does one override the other? If it's the latter, which?

Looking quickly at the trope-pages, they don't seem to me to indicate that the two tropes are mutually exclusive. They point out that their tropes are different, covering different situations—but there's nothing that I see to indicate that those situations couldn't both occur in the same narrative.

("Never Suicide" does mention "significant evidence" being present in the case of "The Coroner Doth Protest Too Much"—but I could see that evidence coming to light as the result of someone setting their mind on "Never Suicide" and uncovering said evidence. Or, alternatively, the "Never Suicide" could be in part a response to "The Coroner Protesting Too Much".)

Thanks!