Is Order Important?

So, I was sitting down to dinner a couple of nights ago and the phone rang. Call Display told me that it was a bank calling. I'd normally just ignore a call from a business at that time of day, but when it's a bank, it could be something important, right? With thoughts of "we've noticed some unusual credit card activity...", or mystery deductions from my account, or maybe an exciting job offer, I decided to answer it.

Nope. No important customer service news.
They just wanted to tell me about an incredible new insurance product.

This was the first time I'd heard about this product, and I might even be in the market for something like this. But I lost interest immediately.

Why make an initial contact with customers using one of the single most hated and annoying marketing vehicles on Earth? I interact with, and receive communications from, this bank in a variety of ways. I log-in to my online account fairly regularly. They send me e-mails. They send me printed statements. I subscribe to their e-newsletter... Seems like there are lots of other ways for them to reach me.

It seems pretty basic to me: the order in which communication channels are used is as vital as the selection of the channels.

How about raising my awareness of the product via something relatively unobtrusive, like a simple ad unit within their Web site? If it piques my interest right away, I can click to find out more. If I don't care, I can ignore it and move on.
Then maybe follow up with an insert in my next monthly statement and in my next e-newsletter. Tell me a bit more about the product. Include a special offer or other incentive. Again, if I'm interested I can make the effort to find out more.
Then maybe, just maybe, use a phone call as a third contact if I somehow appear qualified or interested based on whatever criteria their database marketing people have specified. (And try not to call me during dinner, but that's an entirely different post).

Obviously, the above is just an example, and isn't always the "right" order.
If something's extremely time sensitive, maybe the phone call should come first.
If the product or offer or message isn't particularly important, don't even bother using more invasive communications tools.
If the message is important but kind of boring, start with a medium that can add some excitement, then follow up with something more descriptive and informative...
Whatever makes some logical sense in each particular case.

My big questions are:
1. What was the genius at the bank thinking when they decided that the call center should be the first point of contact to promote this new product? Are they hoping to rush people into saying "Yes"?

and

2. Does the sales pitch actually work better this way? Maybe I'm just over-thinking it or over-sensitive to this stuff. Perhaps the bank has some campaign metrics that justify this process. But do customers really say "Golly, I was just in the middle of dinner, but if you're selling an insurance product that I've never heard of before... Well, heck! I don't mind leaving the table for a few minutes to talk to you!" ?

I lost a pile of respect for this particular bank that evening. I think that qualifies as a Bad Branding experience.