Yes, it is true, If a person has Iman (belief) and he didn't shirk, he eventually enters paradise.
As said here
None shall enter the Fire (of Hell) who has in his heart the weight of a mustard seed of Iman and none shall enter Paradise who has in his heart the weight of a mustard seed of pride.source
'Ubadah bin As-Samit (May Allah be pleased with him) reported:
Messenger of Allah (sallallahu 'alaihi wa sallam) said, "He who bears witness that there is no true god except Allah, alone having no partner with Him, that Muhammad is His slave and His Messenger, that 'Isa (Jesus) is His slave and Messenger and he (Jesus) is His Word which He communicated to Maryam (Mary) and His spirit which He sent to her, that Jannah is true and Hell is true; Allah will make him enter Jannah accepting whatever deeds he accomplished" - [Al-Bukhari and Muslim].
Another narration in Muslim is: the Messenger of Allah (sallallahu 'alaihi wa sallam) said, "Whosoever testifies that there is no true god except Allah and that Muhammad is the Messenger of Allah, Allah (SWT) saves him from the Fire (of Hell)". source
also this hadith which is recorded by Imam Muslim
Jabir (May Allah be pleased with him) reported:
A bedouin came to the Prophet (sallallahu 'alaihi wa sallam) and asked him, "O Messenger of Allah, what are the two imperatives which lead to Jannah or Hell". He (sallallahu 'alaihi wa sallam) replied, "He who dies without associating anything with Allah will enter Jannah, and he who dies associating partners with Allah will enter the Fire". source
So, I hope you find the answer. It is the reward of belief and don't take it lightly. There are many hadith on this.