Do leaves really always have an axillary bud at the base?

[VVD]

Would love some clarification: We're always taught that you can tell a leaf by the axillary bud where the petiole connects to the stem. But what if the axillary bud has developed into a stem/branch? Would it be correct to say that leaves often lack axillary buds at their junction with the stem (maybe one used to be there, but later developed into a stem/branch)?  

Thanks!