Pretty sure you’re right - there’s the concern of the resources / energy needed for recycling but also, recycling decreases the need for new materials enough to offset that.

That said, AFAIK paper and cardboard are the only thing that can be both composted and recycled, so the advice of the person you replied to is still generally good.

This is the guidance I’ve seen on the topic:

Recycle:

• clean, dry paper
• clean, dry cardboard

But compost:

• soiled and wet paper/cardboard
• pizza boxes and other similar things
• paper towels
• paper/cardboard egg cartons

Don’t compost (throw away if unsuitable to recycle):

• glossy paper
• paper with plastic attached
• anything (e.g., paper towels) with cleaning chemicals or other substances unsuitable for composting on it