Is the hybrid-pi parameter hie really equivalent to (beta+1)*re?
To be more precise the \$h_{ie}\$ is not strictly equivalent to \$(\beta+1)r_e\$. 

\$h_{ie}\$ also known as \$h_{11}\$ comes directly from a two-port network theory. Where they treat the transistor as a black box. 
http://ux.brookdalecc.edu/fac/engtech/andy/engi242/bjt_models.pdf

On the other hand, the \$r_e\$ is coming directly from the Shockley equations. 

But despite this in hand calculation, we are using this approximation

\$h_{ie} \approx r_\pi = (\beta+1)r_e\$ in small signal analysis (when BJT working in linear/active region).  

But BJT also has some "real" resistances "built into" the BJT's terminals. 

The base spreading resistance (\$r_{bb}\$) 

https://4donline.ihs.com/images/VipMasterIC/IC/ONSM/ONSMS04099/ONSMS04099-1.pdf?hkey=EF798316E3902B6ED9A73243A3159BB0 (figure 5)

And "bulk" emitter resistance around \$0.5\Omega\$ for small-signal BJT's.