If sp_recompile is placed inside of stored procedure it will actually recompile the next time it runs. From here, for the current execution it uses the plan compiled at previous run. So it's still unclear how it solved the problem. As it was mentioned by other members above, to use WITH RECOMPILE clause would be more beneficial.

Anoter benefit of using WITH RECOMPILE is that it instructs engine not to place execution plan in procedure cache, thereby saving on overhead of placing it there.