Not only does ISO have clear copyright to their published symbols, they are very careful to publish the specific individual use license terms in very clear language:
3: Single User Licence
ISO publications can only be bought for your personal individual use and cannot be transferred to another user. If you wish to purchase (an) ISO publication(s) for multiple users (for example, for your colleagues or post on your company’s intranet) or want to obtain broader rights beyond your personal use, please contact us or your ISO Member to explore your options.
Then there is this section:
6: Codes and Graphical Symbols (and their Collections)
You may use codes (such as language, currency, and country) and graphical symbols for the implementation of their respective ISO standard(s). For example, this means using the symbol in accordance with its meaning as a graphical symbol, e.g., the “No smoking” symbol to designate a non-smokers’ area. However, you may not post or resell these on the Internet. If you would like to use the codes or symbols differently, please contact us or your ISO Member.
These are easily found in public-facing pages here:
So, given the clarity, ease-of-finding, and the fact that we are talking about not only an, but the International Standards Organisation, I think it's safe to say they have some of the best lawyers on Earth, and they will have been very methodical in crossing every t, dotting every i, and thinking through every legal eventuality, every IP use-case, and having appropriate language or contract codicils all pre-canned, ready-to-go - hence their reference to contacting them for nonstandard use-cases.
I am not a lawyer, nor do I play one on TV - I am a multi-decade graphic designer, technical illustrator and technical author (amongst other things) and I can tell you my approach to this sort of thing: buy the symbols's use-rights, read the license and adhere to it, and pass the cost on to your client directly in an itemized invoice, so that they can see clearly you complying with appropriate IP terms and ISO standards. This should reassure them with regards to your professionality.
And as a closing thought here: regardless of fine-points legalities, how would you feel if later, after your nitrile glove packaging design was client accepted and used, and gained popular recognition, some other designer asked your advice (not knowing you designed it) about directly imitating part of that design for their design and whether that was legal... your proper answer should be:
"probably not, but even if it were legal, it wouldn't be ethical."