Instead of taking them to lunch, you should just pay for an hour with them and then spend that time just talking. That way, when they go on about how it's not always about sex and some people just spend the time talking to them, they'll finally have an example of a time that this actually happened.
They'll likely have plenty examples of that already. You've evidently need to take one to Burger King and learn this for yourself.

You'll hear some recollections about sad and lonely old men who want a hug and somebody to talk to because nobody will hear them anymore. You may be shocked how often sex workers wind up working as high priced amateur therapists.
PS - Did ya ever notice that Therapist is one space away from The rapist?
Ya, that was my point. I'm skeptical about the veracity of these claims. It would be nice to give an opportunity to talk about a case where it actually happened instead of pretending it happened to them as opposed to their co-worker's roommates second cousin.
If you don't believe them now, regarding guys other than bip, would you believe them regarding bip after he takes them to burger king? If so, why? What changes other than one more story from somebody you don't believe?
If you really want to see if this is true or false, then maybe you should dress yourself up as one of them and find out for yourself? It is usually the less attractive sex workers who get a higher percentage of this sort of client. Keep at it for a while and I am confident that you will prove to your satisfaction that this does indeed happen. I myself am convinced it happens because I have seen it first hand numerous times, and some of the girls have difficulty handling that part of the job. I've known some over-sympathetic dancers who have left the industry over it, going home feeling sad not because they are being groped nightly, but because they are too often told sad stories from broken men.
Or if you are not comfortable cross dressing, then maybe eavesdrop at a Japanese hostess bar or some strip clubs in America, and hear emotionally vulnerable old men spill their guts out to young strippers, get a pep talk from an attractive (or sometimes not so attractive) woman, and feel better about themselves and listened to. Sex workers encounter emotional needs frequently, and those who can soothe them, often just by being a good listener, can make a lot of money, even if they are not the most attractive girls in the club, and even if the guy never has sex with them. It does happen.
It is easy to paint the sex industry as abusive sex traffickers enslaving women for the exploitation of predator males seeking dominance, but that isn't anywhere close to the whole story of what happens in it.
And last but not lease, why SHOULDN'T sex workers be believed? Why not take them at their word on this? What reason do they have to lie about having some of their customers who just want to talk? It isn't like they are saying that's the norm. They are just saying it happens... because it does.
Sex workers get shat on constantly by society. They get abused by pimps. They get used by johns. They get disbeleived by you. They get ignored by government, who puts them at risk of physical harm in unsafe working conditions to satisfy demands of the religious and the "feminists". Many of them fall into a fast life of easy money and fall into drugs and get accustomed to having that money, which disappears once they hit a certain age or get a disease, and they hit a brick wall, having no above board work experience and a gaping hole in their resume, only to now get a minimum wage job, if that. They get socially programmed, more than anyone else in society, to equate their self worth with their ever declining physical appearance. I do think some sympathy is in order here. Taking an ex-prostitute out to lunch isn't a bad idea. Taking a lonely old man or woman out to lunch who will otherwise go ignored is too.