If you are currently registered for an account with firstname.lastname@example.org, and your company created a separate account, they cannot invite your email email@example.com and will receive an error message.
If you would like to join a different Nimble account, there are two options:
Export your data out of your account and then delete the account. This will free up your email and allow you to be invited to your new account. How do I export out of Nimble?
Change your login email in Settings >> My Account >> Change Email for your current account so your company can invite firstname.lastname@example.org.
Note: if you are a Google Apps user, you will need to contact email@example.com to change your account username.