A buyer can click on Send Offer without putting the item in their Watch List.
Your offers get sent to buyers who satisfy a number of conditions including:
1. They haven't received an offer from you for the same listing previously.
2. They haven't purchase the same item from you previously
3. They're watching your item
4. They've had the item in their shopping basket for a period of time
5. They've viewed your listing multiple times
6. They're a buyer in good standing on eBay.