Before starting, AMD signed an agreement with Intel that gave them an explicit license to x86. And x86 was a whole lot smaller and simpler back then in 1982. A completely different and incomparable situation.
Technically it was after starting - AMD was founded in 1969 as a second-sourcer for Fairchild and National Semiconductor, and had reverse-engineered the 8080 by 1975 and acquired a formal license to it by 1976.
The 1982 deal you speak of was actually pretty interesting: as a condition of the x86's use in the IBM PC, IBM requested a second source for x86 chips. AMD was that source, and so they cross-licensed the x86 in 1982 to allow the IBM PC project to proceed forward. This makes the Intel/AMD deal even more important for both companies: the PC market would never have developed without the cross-licensing, which would've been bad for all companies involved. This gave Intel an ongoing stake in AMD's success at least until the PC market consolidated on the x86 standard.
