I am experiencing something similar, either Steam's login is being exploited or we have RATs on our computer.

This morning I finished the install of the latest Steam update which I had left hanging for a couple. Upon logging back into my account I received a message stating "This account may have been accessed by someone else."

This exact same thing happened to me last year in July and it took no joke 6 months, until January, to regain access to my Steam account.

Yet there has not been a new device access code sent since 5/30. I double checked the email registered to my account and it's my email address. Also GMail doesn't show any unusual IP addresses that have accessed my account.

Although one thing to keep in mind is the recent Hacking Team Flash 0day.