I don't think that cards that earn points that are able to be converted to Hilton should count as a "Hilton" card.

Amex MR converts to Starwood points (although at a very bad rate), but it's not counted as an SPG card. For SPG there are 2 Amex cards - personal and business - and that's it.

When counting Hilton cards you should only count those branded at a Hilton card. I have nothing against Hilton and have both the Hilton and SPG cards from Amex, but I do tend to heavily favor the SPG card because the wider variety of redemption options available.