I wouldn't suggest lying to your customers at all, but if I were dropshipping, I would not go out of my way to divulge that information openly.
Why do some customers have a problem with it?
Well when you purchase something from a business and have an issue with it, you can go straight back to the business and lodge a complaint to have the issue resolved. Most consumers want that direct access to get a resolution to the issue asap, however with a drop shipped product, they know they aren't buying from the actual retailer themselves.
Now they are in a position where they are relying on you to then get the issue resolved for them and that is uncomforatble because they aren't able to control the situation and they have no idea if you will be able to or not, so there is a massive unknown factor with purchasing through dropshipping with a lot of customers and the one thing that most consumers look for in a purchase is CONFIDENCE!
Remove that confidence and you remove the sale.
Regarding answering questions. Product knowledge is one of the most important things in sales and while you may not be selling face to face, make no mistake about it, you're still working in sales. So it's important to gain as much knowledge as possible about the products you are marketing. That said, I wouldn't suggest putting a number, email is fine.
Ultimately, your listing really should be informative enough for a potential buyer for them to not even need to ask you any questions. So you really need to focus your attention on providing a quality listing that answers everything for the customer. Remember, if you're selling on a platform like an eBay, then it's quite easy for a customer to go to the next seller who is selling the same or very similar to you to find the information that you haven't provided them in your listing and once they do that, they won't come back, they'll just buy from your competition.
So it's important to consider all of these factors and leave nothing to chance, because boats don't float for long with holes in them :)