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FORTUNE — We hear a lot about entrepreneurs who don’t want to take their companies public, but who ultimately give in to arm-twisting by their venture capital investors. Never, however, does that reluctance make itself known in the actual offering prospectus. Well, almost never.

Take a look at the following item from an S-1 filed by medical device company Applied Medical Corp., whose largest outside shareholder is Institutional Venture Partners:

“Institutional Venture Partners IV, L.P. is compelling us to register the shares of Class A common stock offered hereby by exercising demand registration rights. While we intend to comply with our obligations under the Master Rights Agreement, our board of directors and executive officers believe that filing the registration statement of which this prospectus is a part and effecting an initial public offering of our Class A common stock are not in the best interests of Applied.”

That’s right: IVP is forcing one of its portfolio companies to list shares, and the company wants everyone to know about it. This is remarkable and, from what I can tell, unprecedented.

To be clear, almost every venture investor has the legal right to force such a sale. It’s a standard term sheet item called “demand registration,” but the VC attorneys I’ve spoken with say that they’ve only seen it used as an idle threat. After all, who wants to road-show a company whose senior management refuses to participate?

So why is IVP doing this? Here is the explanation from IVP founder Reid Dennis, as part of a video message posted on the website of underwriter WR Hambrecht (which was chosen by IVP, not by Applied Medical):

“We invested, through one of our funds, IVP IV, we invested in Applied Medical Corporation twenty-four years ago, when it was a start-up enterprise, and we led the follow-on financing twenty years ago. Now, this is a very successful company. They are in a highly competitive industry and yet they have become the low-cost producer. Applied Medical Corporation has done all of its manufacturing essentially in Southern California in their own plants and in their own owned-plants.

The problem we have is that IVP IV was supposed to be a ten-year fund, which is standard in the venture capital industry, so twenty-four years is a long time to try to keep maintaining a fund that was supposed to last for ten years. Our investors, some of them have had a real need for liquidity. These investors include a major bank, which you would all be familiar with; two major university endowment funds which would be familiar to you; several large insurance companies, and a major corporation’s retirement plan. Some of these investors, our investors that invested in our fund have had to sell their holdings in IVP IV at a very, very substantial discount from what the true value should be. And that is really painful, to them as well as to us. None of us who are closely associated with Institutional Venture Partners are anxious to sell our investment in Applied Medical Corporation. I would like to continue to hold onto the stock that I own in this company as long as I can and I would love to be able to make gifts of it to my children and my grandchildren. Because I think it has a long way to go as a growth company.”

Neither Applied Medical nor IVP are commenting on the situation, so we’re left right now with a lot of questions.

The most obvious is why Applied Medical doesn’t want to go public? It’s a mature company whose revenue climbed from $282 million in 2010 to $350 million in 2011, with its net income more than doubling over that period from nearly $21 million to over $44 million. Not saying it would be Workday Redux, but clearly there is a legitimate growth story here.

It’s also unclear why there hasn’t been any sort of sale process. Applied Medical’s founding CEO Said Hilal has suggested in newspaper interviews that his company wouldn’t currently be a good fit with larger strategics – perhaps because its success is largely predicated on undercutting such competitors on price —  but what about private equity? Or what about IVP selling its minority stake on the secondary market?

All I can guess is that Hilal doesn’t want anyone else calling the shots, and he has enough shares to prevent a change-in-control. Maybe it’s because he honestly believes someone else will mess up his business. Or perhaps he doesn’t want to risk a change to his lucrative personal compensation ($875k base for 2012, plus an $850k 2011 bonus and untold dividends). Moreover, no one is going to buy IVP’s stake on the secondary market if it doesn’t see a reasonable path to exit.

I’m also not sure if IVP is even going to succeed in the public offering. The original S-1 was filed over a year ago – yes, I’m late to this story – and Applied Medical since has accused WR Hambrecht of possibly “taking actions that are not in the best interests of us, our stockholders and potential investors.” The SEC has asked questions about that situation – which includes some third-party research Hambrecht posted on its portal – and I’d expect more clarity soon.

Also worth noting that there is pending litigation between Applied Medical and the IVP partner who led the deal (Peter Thomas, now with another firm), related to the company’s internal valuation and shares repurchased by Thomas.

So consider this a story in process, rather than one with conclusion. But there is at least one lesson: Entrepreneurs don’t always have to do what their VCs say, and VCs don’t always succumb to the PR pressure of looking entrepreneur-friendly.

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