Well the rumour is wrong, I quite frankly searched it up. I got the answer that Cap still wasn't fully worthy yet because of the fact that he is still keeping in the lie about tonys parents death.

I think it's true. Captain America could have picked uo Thor's hammer - but I think he didn't do it for two reason. One reason is yours. Another one is - HE FELT NOT READY.

According to Joe Russo, Captain America had the power to lift Thor’s hammer in Age of Ulton, but pretended he couldn’t to keep Thor happy.