Recently, on an item for sale for $50 with a best offer option, when I entered $40, a prompt automatically came up on the screen indicating that the seller is more likely to accept an offer around $45. How truthful or reliable is this message, or is it a subtle way for eBay to make more on fees by encouraging higher best offers, and hence should be ignored by buyers?
Ignore those messages from eBay. They are bogus AF. I see them as both a seller and a buyer. The messages to buyers always suggest making a higher offer, and the messages to sellers always suggest pricing items lower or making lower counteroffers.
Those messages are created by eBay for the benefit of... eBay. Period. They do not have buyers' or sellers' best interests at heart, only their bottom line, so their algorithms will recommend ANYTHING to increase the likelihood of a sale.
Offer what you feel appropriate, regardless of what eBay recommends.