What does that's as may be mean?

It means "that may be so" or "that may be the case." It's more common in British English. Reference these lyrics to The Who song, "I Can See for Miles."

I saw you holding lots of other guys

and now you've got the nerve to say

That you still want me

Well, THAT'S AS MAY BE

Because all the while

I can see for miles and miles

Pete Towshend