I can also confirm this. I currently have the following:

1 personal charge (plat)
1 biz charge (gold)

5 personal credit
2 biz credit

I applied for the Gold Delta SkyMiles 50k miles offer on Saturday. Just got a call from Amex underwriting letting me know that while I could get approved for it based on income, credit, history with Amex, they can't approve it because I'm 3 over the 4 credit card limit. I'd have to close four (4!) cards in order to get approved for the Delta Gold card.

I passed.

(For context, I ended up with that many Amex CC's from well before they instituted the 4 credit card limit.)