That is correct, PSEXEC is to be launch with elevated rights, in addition to this PSEXEC is also to be copied to the SYSTEM32 folder on the remote server.
I know it works because i use it :)
I hope this helps.
Michael

you can run cmd in elevated mode to run psexec

see https://www.experts-exchange.com/questions/23127265/Launch-CMD-on-remote-computer.html

From a run prompt you can also launch cmd locally as an admin on a remote server using the below:-
runas /user:DOMAIN\USER cmd
When this is running as the Administrative account, you can then use PSEXEC and launch CMD without further usernames or passwords.

Assume that you are currently sitting at, or logged in to the local computer, computer A.  You want to use psexec to run a process on computer B which is the remote computer.

First step:
psexec is a program and runs locally on computer A.  It has to execute to be able to do it's fun remote magic.  So it will run as the locally logged on user unless you do run it special like using runas as MichaelIanClaridge posted above.  If the user running psexec doesn't have the correct permissions to run psexec as a program locally then you will be denied permission.

Secondly:
psexec runs on computer A, but connects and starts to make changes to computer B.  When connecting to computer B psexec will use the current user account running psexec, or the user specified by the psexec "-u domain\user" parameter if it was supplied.  This means psexec needs to either be running on computer A as a user with admin rights to computer B or needs to have been started with the -u parameter to specify an admin user on computer B.  If not, you will also get permission denied.

If you wanted to copy the text in your command prompt when you try to run psexec we can help pinpoint where the issue is and help provide the correct solution.  Right click in the command window, select "Mark".  Then highlight the text and right click to copy it to the clipboard.  Then you can paste it here.