One possibility: The 32-bit programs path on 64-bit Windows is typically "C:\Program Files (x86)" rather than "C:\Program Files".
VBP is invoking PsExec to actually run the program remotely, so you would need to contact
SysInternals support about getting more error information or details on why the bittedness of the remote computer would affect PsExec and/or your program. To reproduce the problem outside VBP, create a new text file and copy/paste the logged PsExec command-line followed by
echo %ERRORLEVEL%
into a .bat file and run it from a Command Prompt.