Your assumption about all modern tuners accepting digital cable/OTA is incorrect.
First, I think you misspoke when you said digital cable. Why are you interested in digital cable when you have analog cable? Second, no current tuner can record digital cable unless you rent a Cable Card from your cable company and buy a tuner that can accept a Cable Card. Third, some tuners are ATSC only (OTA only) which means they will not be able to record analog cable.
So, in summary then, if you want to record analog cable and OTA, you will need to look at the available tuners very closely to make sure they can record both. The ASUS card that you linked to appears to be capable of recording both analog cable and OTA, but can definintely NOT record digital cable channels (ones you need a box to decode).