... But some day, your jurisdiction, your county, your state, or even our Federal Gov't may require that homeowners, for whatever reason, must disclose if there are friable or non-friable products sealed, or otherwise, in the home. IF you were to put up 'anything' over top of asbestos, thus, sealing it in, and a homeowner some time later was to discover this (after you've sold and moved), you could be sued. It happens today with lead paint abatements. It's quite possible it could happen with non-friable asbestos.
My free, unsolicited advice: Now that you have more information about asbestos siding (non-friable asbestos), you can tell 'people' that, yes, you can install many types of siding over top of asbestos shingles BUT, (what I just said above may occur in time.)
It's not so clear cut from where I'm sitting. Here in PA, the state legislature is considering that this type of siding be labeled as hazardous. It only needs to be voted on. AND, to boot, this state is considering making the Seller Disclosure Form a REQUIRED Condition Of Sale. There ya go!
And lastly, sure, you can put vinyl siding over top of this stuff. BUT, if you read the Warranty and/or the Installation Instructions, you can void it by doing such. In short, it, in particular, must be installed over a FLAT surface. Many sidings are not considered FLAT. It would be best to talk to the mfgr. to see if they'll warranty the product in a particular condition. A contractor will say, "Sure, I'll warrent the work." BUt in a year or so, he may be out of businees. Plus, even if he's still in business, after you talk to the mfgr., they'll say your beef is with the Installer! He installed it; NOT the mfgr.
I'm just trying to make you more informed. My best to ya and hope this helps.