You didn't mention trying Fedex. If you had done that in the first place, you'd be typing a complaint about Fedex instead. Though it's typically not difficult to understand, you will have the same confusion with all shipping companies. It should also be common knowledge that the post office (USPS) doesn't offer any such service. Accounts need to be set up for billing purposes. Credit needs to verified and established before UPS or Fedex will be sending drivers around town for what may be invalid customer credit. That shouldn't be too hard to understand.
What you were trying to do was set up a service called a Call Tag. There are two main options for a Call Tag, those being a 1 Pickup Attempt and a 3 Pickup Attempts. If the package is not ready at the pickup time, the pickup fee is still paid. There is a pickup fee for both UPS and Fedex to cover the cost of a truck and driver to go to a location for a pickup. And no, UPS, Fedex, or USPS do NOT pre-print labels for you. A label still needs to be created and adhered to your package. First off, why wasn't the person shipping you the package willing to take care of the shipping, and you could have reimbursed?
Since you were already in the UPS website, why didn't you print a label out and then either email, fax, or mail the person your shipping label that would be billed to your credit card? Still, the easiest way would have been to have that sender bring it to a place like The UPS Store and simply send it to you. You would have saved over three hours of phone minutes and the shipping cost would have been far less at a UPS Store than online with a pick up. Even with the markups at non-UPS locations, it still would have been cheaper and less hassle.
No UPS operator will state a time of day when a delivery or pickup can or will be made. It is not possible to assign an exact time. The number of deliveries and pickups, signatures, road and traffic conditions, etc, etc, make the Drivers for ALL carriers begin a saturated route in the morning at their respective hub facility and make as efficient route or 'loop'. Obviously, no carrier truck could get the hundreds of daily deliveries and pickups if he had to zigzag all over a city in a random order to accomodate a specific time for each.
It appears that the problem is with an inability to understand how shipping works and/or a communication breakdown on a phone. At times, I see in my business a customer that gets it in his head to do one thing a certain way, then just doesn't get it when someone tells him it needs do be done differently. This chore you needed to accomplish is a simple task with UPS, but thus far a solution can't be done simple enough for you.