Consider the recommendation if the candidate can show how the work would get done with less of their time. Ask for a written plan before changing your hiring decision. A preference for part-time work, by itself, doesn't establish that it fits your business.
I recorded some feedback about this exact conversation. Someone was concerned about applying for a full-time role and then suggesting a shorter engagement.
The important part of my advice was that the operator has to know enough about the business and the position to make an honest recommendation. You can't arrive with the answer before you've understood the work.
The wording I suggested was: “After learning about what you guys need, I have to tell you, I don't think you should hire me for this full time.”
That's a recommendation to examine. It isn't a reason to skip the examination.
Ask what changed their view
You've advertised a role because something needs attention. A strong candidate may see a narrower assignment than the job description suggests. Ask them to explain the difference.
Which responsibilities require their experience? Which need daily execution? Who would handle that execution? What would still come back to you?
The answers matter because a smaller commitment to the candidate can leave a bigger commitment for your team. If the proposal only works because you silently take over the remaining responsibilities, you haven't established that it solves your problem.
I'd also ask what they've learned that supports their recommendation, and what they still need to check. Experience can inform the plan. It shouldn't become an excuse to leave the plan unexplained.
Put the alternative on paper
In the same feedback, I suggested the next step: “Let me put pen to paper and let you know what I would do to get this outcome for you.” Then walk through it together.
Use that discussion to connect the outcome, responsibilities and available time. Be explicit about the work left with your team. Compare the full cost of each arrangement, including any execution help the fractional proposal requires.
If the work needs dedicated daily leadership, keep that requirement. If the plan shows that experienced ownership of a narrower assignment is enough, fractional may be worth considering.
You don't have to defend the original job description. You do need a credible answer to who will do the work.