The laptop would often be a MacBook Pro.
Some Apple products will enable HDCP simply by being connected to a HDCP compatible input regardless of whether the content calls for it. Unless you need the computer to be able to play back HDCP protected content you might want to see if you can turn off HDCP for that input. In fact recording protected content seems to open up a number of potential issues and unless you really need to support playback of protected content you might be able to disable HDCP in general.
Will this capture card be viewed differently by the sources than a monitor or repeater? In other words, COULD a computer's HDMI output refuse to send ANYTHING, copy protected or not, because the destination is a recorder?
In your case the AMX is handling the EDID and HDCP management and it could refuse to send any protected content to that output.
Perhaps another way to look at this is that if content is HDCP protected then the intent may be for it to not be digitally recorded so you may need to look at whether you are trying to address an unintended effect of the HDCP or to potentially subvert the intent of any copy protection.
Would I be better off with an HD-SDI capture card or VTR and scaling/converting the 2 computer's digital outputs to HD-SDI, stripping them of HDCP? Or is that technically not legal to do so?
The HDMI-to-HD-SDI devices are typically HDCP compliant in that they will
not accept HDCP protected content and may tell the source to not send them HDCP protected content. When I have talked with Blackmagic, Grass Valley, Aja and others about their converters they have all said that their products will not support being used as HDCP strippers as that would be effectively bypassing the copy protection.
PS - since I really don't know enough about HDCP, can someone recommend a place to learn? I'm going to look through support pages on Extron/Crestron/AMX web pages to see what I can learn. Wish there were a video equivalent of Syn-Aud-Con.
All three of those manufacturers as well as others such as Kramer Electronics have both online and classroom offerings on digital video. While some of them tend to focus on their products, all of the related classes, workshops, etc. I've attended from those parties have included at least some general content.