The answer is 'most likely YES. I'd recommend you sit down with either a Business Law attorney or better yet an Intellectual Property attorney and explore the options. It may be possible to enter into a contract in which the product you are using in your own sales can be 'licensed' such that applying your own company's logo on the product would be acceptable to the seller from whom you are purchasing it. The attorney can work out the legal parameters of this purchase so that later you are not facing a lawsuit. Good Luck on this !
If done pursuant to an agreement with the product manufacturer, then I agree with Counselor Potter that there is almost certainly a legal way to do this. If I understand your intent, it would be either some version of an outright Original Equipment Manufacturer (OEM) deal, or something very similar to an OEM deal. These occur with great frequency and with all sorts of products.
I'll just note that if you took it upon yourself to switch out the branding without permission from the actual manufacturer/source, this would constitute "reverse passing off" of the actual source's product as your own, hence impermissible.
So strictly from a CONSUMER PROTECTION perspective, why is an OEM arrangement which has been sanctified through a contractual arrangement legal (and extremely common), while even a painstaking and conscientious effort by one business to locate, test and quality assure the product(s) of another business, then purchase and UNILATERALLY rebrand those products with its own mark? I don't have a pat answer to this question. To remain consistent here, perhaps we are forced to acknowledge that the doctrine of "reverse passing off" is not intended to protect consumers at all, but ONLY to protect the source business(es) whose goods are rebranded without their permission...
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Like you similar question, I see no danger on the few facts you post. Your "sold under a brand name" is a little ambiguous, and it is hard to tell if any trademark (unregistered) is "generic" or the pack is "generic".
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.