Their decision was based on what we would today call a fundamentalist or literalist reading of Scripture, but the in my view the main reason for taking this decision was that Bellarmine believed that neither the Ptolemaic nor the Copernican theories corresponded to physical reality, but were only calculational tools to ``save the appearances.'' He doubted that there would ever be a scientific proof one way or the other, and therefore he considered it the safest course to simply condemn what seemed to be a dangerous opinion. The modern mind may find it difficult to see what dangers Bellarmine saw lurking in Copernicanism. But in his time, the notion that ``nature does nothing in vain'' was accepted without question. A cosmology in which the planets are not like the stars but like the earth implies that these bodies must be inhabited, raising all sorts of difficulties for the Catholic doctrines of original sin, the Incarnation, and the Redemption.
Some commentators have tried to defend the Inquisition's decision by pointing out the flaws in Galileo's evidence, and it is true that his case was by no means proved. For instance, he continued to assume that the planets' motions were circular. Kepler had already discovered that planetary orbits are actually elliptical, but in the absence of a theory of gravitation Galileo considered this idea physically absurd. Thus he was forced to retain the same cumbersome epicycles as the Ptolemaic theory. Doubts about Galileo's discoveries were also raised because telescopes of the time were still quite primitive. Defects in the lenses or non-uniformities in the glass produced artifacts, so it was not always certain what was real and what was an optical illusion. Repeated observations by different people and using different instruments could sort this out, but one-shot demonstrations could leave skeptical people unconvinced.
But ultimately, the theologians, including Bellarmine, simply did not trouble themselves to grasp Galileo's arguments. The Inquisition's decision was based not on the merits of the scientific arguments, but on a failure to recognize the autonomy of science as a genuine source of truth, independent of Scripture. The Inquisitors did recognize that they were not competent to evaluate the scientific case. They followed proper procedure by requesting expert opinions on the matter. Perhaps if the scientific experts had been unanimous in their support of Copernicus, the theologians would have bowed to their authority. But the scientific community was divided on the subject, and so the condemnation proceeded.
Having reached a decision, the Sacred Congregation of the Index published a decree condemning the ``... doctrine, altogether contrary to the Holy Scripture, that the earth moves and the sun is motionless.'' Foscarini's book was prohibited, and Copernicus' book was suspended pending correction. Galileo and his books were not explicitly mentioned. However, Galileo was called to a personal interview with Cardinal Bellarmine at which he was informed of the content of the decree and told to obey, and he submitted. There is some question about exactly what he was told in this meeting. The Cardinal held no office in the Inquisition, and so his role would have been merely to convey the decision to Galileo and obtain his assent. However, the Inquisition file on Galileo contains a memorandum or minute of this meeting, which states that besides Bellarmine, the Commissary of the Inquisition and a notary were present. Presumably they were supposed to deliver a formal warning with the authority of the Inquisition only if Galileo demurred after Bellarmine informed him of the decree. But according to the minute, after Bellarmine told Galileo that the decree forbade anyone to ``hold or defend'' the Copernican doctrine, immediately, without giving Galileo a chance to respond, the Commissary gave him a stronger injunction ``not to hold, teach, or defend it in any way whatever, either orally or in writing.'' This minute is not a formal judicial document. It is not signed by any of the participants. Some commentators have speculated that it was forged and placed in Galileo's file to incriminate him later. Others suppose that the Commissary took it upon himself to make sure that Galileo received the stronger injunction regardless of his response to Bellarmine's informing him of the decree.
Galileo took the precaution of obtaining from Bellarmine a certificate describing what occurred during their interview. This certificate only mentions Bellarmine's warning not to ``hold or defend'' the Copernican theory, and not the stronger injunction recorded in the minute.