Receptacle connection with aluminum wiring?
First off, the first electrician is wrong in saying that the use of a crimp-type terminal in house wiring is categorically unsafe.  Crimp-type terminals listed under UL 486A for use on solid wire of the given gauge are considered acceptable for use in building wiring, as per UL 486A section 1.1:


  These requirements cover pressure wire connectors and soldering lugs for use 
  with copper conductors according to the National Electrical Code, NFPA 70.


and NEC 110.14(A):


  Terminals. Connection of conductors to terminal parts shall ensure a 
  thoroughly good connection without damaging the conductors and shall be made 
  by means of pressure connectors (including set-screw type), solder lugs, or
  splices to flexible leads. Connection by means of wire-binding screws or studs 
  and nuts that have upturned lugs or the equivalent shall be permitted for 10 
  AWG or smaller conductors.
  
  Terminals for more than one conductor and terminals used to connect aluminum 
  shall be so identified.


However, I would be quite hesitant to call this specific application fully Code-conformant -- garden-variety listed crimp terminals are listed for use with copper wire only, and it would be unlikely that the previous homeowner had access to terminals identified for use with aluminum wiring.

EDIT based on updated info about the devices:

Since the existing devices are copper only, your options go as follows (in order of preference):


Find an electrician in your area who is qualified on the Tyco/AMP COPALUM system for pigtailing copper to aluminum -- these have a long, successful field service history, but require a specially qualified electrician to install, and are rather expensive -- you might be able to get the seller to shell out for this, though...
Use the AlumiConn connectors with a torque screwdriver for pigtailing.  This is something that most electricians can do, or you can DIY if you know your way around electricity and have a torque screwdriver -- the AlumiConn must be torqued to spec to meet its UL listing.
Replace all the devices with modern CO/ALR types.  This is a last resort as CO/ALR device performance has been historically variable, unfortunately.