NO,not mere Hindu beliefs.That Shalagramas and Banalingas are really "Swayambhu" in nature are facts which are confirmed in Scriptures.
For,example,the following Sloka found in the Skanda Purana,confirms that Shalagramas are Swayambhu:
Shlalagramasilaayastu Prathistha Naiva Viddhate(Skanda Purana)
For Shalagrama Sila Pranaparthistha is not required.
Similarly,the following Sloka,from Bhavishya Purana,proves the same for BanalaingasBanalingas:
Banalingani Rajendra Khyatani Bhuvanatraye ||
Na Prathistha Na Sanskara Stesham Na Avahanam Tatha(Bhavishya Purana)||
The Banalingas are famous in the three worlds.They don't require Pranaprathistha,Sanskara or Avahanam.