I am referring to telemarketing calls. Nearly all of those I encounter are live; rarely do they leave a message. The most recent I got was earlier today, and about one second in the person at the other end said "Capital One". That's a credit card company, and bingo, I know on whose behalf I'm being spammed, regardless of whether they blocked Caller ID.

In fact, I can only recall two campaigns of spammy phone calls where messages were left if I wasn't there to take the call live.

The first of those was years ago, and consisted of a robot (an obviously synthesized voice) claiming that I had an "important message" from some person whose name sounded French. It left a number to call back and didn't explain anything about the nature of their business, including mentioning any products. In other words, it was fairly consistent with your description. (Needless to say, not knowing what business they wished to discuss and the calls being unsolicited, I neglected to actually dial the number provided. Since it was a robot, even if I answered live I got the same one-way spiel and then it hung up; there was no live human to ask questions of.)

The second, more recent, consisted of calls that left the beginning of a prerecorded sales pitch (but with a human-sounding voice) on my machine if I didn't answer it live, running into the machine's message length limit. That one clearly identified a company or product, though I can't recall which.