I think that passage is meant more along the lines of "should your DM decide that use of poison in particular circumstances is not certain to succeed (i.e. dip an arrow head in an injury type poison), and not certain to fail (i.e. trying to put an inhalation type poison on a dagger), and thus an appropriate time to call for some kind of check, you should gain your proficiency bonus on that check if proficient with this tool."
I think this is one of the many cases where specific examples actually serve the opposite purpose - rather than helping uncertain DMs gain certainty and empowering DMs to call for checks and set DCs as appropriate to the circumstances of their individual campaigns, they cause uncertainty or leave a less-confident DM adhering to the examples even when those examples are not fully appropriate for the circumstances of their campaign.Most likely that is the direction of intent, yet vague doesn't quite sum up the information about it. And if that is the original intent, there are no examples in the core books about applying improper poisons or applying them in strenuous circumstances. I doubt it is something that would ever come up in my own games, but it would be nice to see clarified for those interested.
I think this is one of the many cases where specific examples actually serve the opposite purpose - rather than helping uncertain DMs gain certainty and empowering DMs to call for checks and set DCs as appropriate to the circumstances of their individual campaigns, they cause uncertainty or leave a less-confident DM adhering to the examples even when those examples are not fully appropriate for the circumstances of their campaign.