So much of an oversimplification of specific claims that the verdict is easy: not true.
What is true:
Very early on in 2003 there were very close matches found of animals being infected with reasonably close relatives of the human SARS-CoV-1 virus strains (Isolation and characterization of viruses related to the SARS coronavirus from certain animals in southern China, 2003). Crucially, at this point such reports also noted too many differences still: "although the natural reservoir is not known."
Evidence as the limited one just listed & speculation about the most likely candidate species already included masked palm civets — but excluded any bats most of the time:
"Our research has shown that the SARS coronavirus found in human victims is the same as the SARS coronavirus found in civet cats," said Wang Ming, an official from the Guangzhou Centre for Disease Control and Prevention.
Wang added that the discovery provided proof that civet cats had spread SARS to humans.
— Qiu Quanlin: "Scientists prove SARS-civet cat link", China Daily, Updated: 2006-11-23 06:52
These early reports were often quite hasty in their conclusions.
That a virus can 'infect' multiple species, or at least 'contaminate' them, does not prove that it originated in this or that species. It merely proved that SARS may jump species. In this case, without establishing a unidirectional route, between civets and humans. And humans are known to have infected some cats.
Severe acute respiratory syndrome (SARS) first emerged in Guangdong on November 16, 2002, and subsequently spread to Hong Kong, Beijing, Taiwan, and other areas. According to WHO, 8 098 cases were reported in 29 countries. Although researchers around the world have been carrying out extensive studies for 10 years, the reservoir of SARS coronavirus (CoV) has not been found.
At the beginning, a virus sharing 99.8% homology with SARS CoV was found in Himalayan palm civet (Paguma larvata). However, it is not the reservoir and the investigation has focused on bats. Some researchers believe that Bt-SLCoV (Bat SARS-like coronavirus) Rp3 (DQ71615) of Rhinolophus sinicus is closer to SARS CoV than other strains, but still not the direct ancestor. Rp3 was supposed to emerge first in 1998, 4.08 (1.45-8.84) years earlier than SARS CoV.
It seems that the great grandfather of SARS CoV has been found but not the grandfather and the father.
Thus, we define Rp3 as “the parental generation (PG) 3” of SARS CoV, leaving “PG 1 and 2” to be found. To explore the cross-species evolution of SARS CoV, studies have been conducted on its major genes such as ORF1a, ORF1b, S, E, M, N, especially gene S and S-encoded amino acids combined with angiotensin-converting enzyme 2 (ACE2). Although some characteristics have been found, scholars still believe that further studies are needed.
— Dezhong, Xu et al.: "SARS coronavirus without reservoir originated from an unnatural evolution, experienced the reverse evolution, and finally disappeared in the world", Chinese Medical Journal: July 5, 2014 - Volume 127 - Issue 13 - p2537–2542, doi: 10.3760/cma.j.issn.0366-6999.20131328
Only as of 2017 is a reasonable 'nearest neighbour'/ancestor characterized:
Increasing evidence has been gathered to support the bat origin of SARS coronavirus (SARS-CoV) in the past decade. However, none of the currently known bat SARSr-CoVs is thought to be the direct ancestor of SARS-CoV. Herein, we report the identification of a diverse group of bat SARSr-CoVs in a single cave in Yunnan, China. Importantly, all of the building blocks of SARS-CoV genome, including the highly variable S gene, ORF8 and ORF3, could be found in the genomes of different SARSr-CoV strains from this single location. Based on the analysis of full-length genome sequences of the newly identified bat SARSr-CoVs, we speculate that the direct ancestor of SARS-CoV may have arisen from sequential recombination events between the precursors of these bat SARSr-CoVs prior to spillover to an intermediate host.
— Ben Hu : "Discovery of a rich gene pool of bat SARS-related coronaviruses provides new insights into the origin of SARS coronavirus", PLoS Pathog. 2017 Nov; 13(11): e1006698.
Published online 2017 Nov 30. doi: 10.1371/journal.ppat.1006698, PMCID: PMC5708621, PMID: 29190287
Earlier speculation about "bats must be it" may seem a either clairvoyant or a shot into muddy waters? But even the "clairvoyant" type of insight isn't knowledge:
Masked palm civets (Paguma larvata) were initially hypothesized to be the animal origin of SARS-CoV. However, since a large number of genetically diverse SARS-related coronaviruses (SARSr-CoV) have been detected in multiple species of horseshoe bats (genus Rhinolophus) from different areas of China and Europe in the aftermath of SARS, it is prevailingly considered that SARS-CoV originated in horseshoe bats with civets acting as the intermediate amplifying and transmitting host. Recently we have reported four novel SARSr-CoVs from Chinese horseshoe bats that shared much higher genomic sequence similarity to the epidemic strains, particularly in their S gene, of which two strains (termed WIV1 and WIV16) have been successfully cultured in vitro. These newly identified SARSr-CoVs have been demonstrated to use the same cellular receptor (angiotensin converting enzyme-2 [ACE-2]) as SARS-CoV does and replicate efficiently in primary human airway cells.
(— Ben Hu 2017)
For the later part of the claim, namely that SARS-CoV-2 origin is still undetermined, it seems one can be quite confident, that bats are not in the frontline of suspects, especially as CoV-2 seems to have quite a difficult time invading natural, i.e.: non-huamainzed bat cells:
Bats are natural reservoirs of numerous coronaviruses, including the potential ancestor of SARS-CoV-2. Knowledge concerning the interaction between coronaviruses and bat cells is sparse. We investigated the susceptibility of primary cells from Rhinolophus ferrumequinum and Myotis species, as well as of established and novel cell lines from Myotis myotis, Eptesicus serotinus, Tadarida brasiliensis and Nyctalus noctula, to SARS-CoV-2 infection. None of these cells were sensitive to infection, not even the ones expressing detectable levels of angiotensin-converting enzyme 2 (ACE2), which serves as the viral receptor in many mammalian species. The resistance to infection was overcome by expression of human ACE2 (hACE2) in three cell lines, suggesting that restriction to viral replication was due to a low expression of bat ACE2 (bACE2) or absence of bACE2 binding in these cells.
— Sophie-Marie Aicher: "Species-specific molecular barriers to SARS-CoV-2 replication in bat cells", bioRxiv, PrePrint, doi: ; this version posted May 31, 2021.