On interpreting this set of curves (Transistor in Saturation mode and decrease of \$h_{FE}\$)
"We  know that \$I_C = \beta I_B \$"...

Wrong assumption! That relation is valid only in the active region, i.e. when the transistor acts as a linear current amplifier.

When a BJT enters saturation its beta decreases quite sharply and the base current ceases to control the collector current.

In other words, the saturated BJT can no longer be modeled as a current controlled current source.