It may help to compare Matthew's account to Mark's, Luke's and John's. A typical translation of Mark's version is:
And he rose, and immediately took up the pallet and went out before
them all; so that they were all amazed and glorified God, saying, “We
never saw anything like this!” (Mk 2:12)
Luke 5:26 treats the story similarly to Mark saying: 'struck with awe, they said “We have seen incredible things today.”' In the account of John 5, the crowd expresses no awe, but "the Jews" react very negatively (some interpreters such as NIV render this as "the Jewish leaders.")
Mark's and Luke's versions are more straightforward and journalistic than Matthew's, reporting what the people said, rather than what they felt. But this does not completely resolve the OP's question, because the people may indeed have said "Praise God, who gives men such authority." Matthew also may be telling us how he understood the reason for their praising God even though they didn't verbally express it. Or, as the OP suggests, he may be expressing his own opinion about why God deserved praise in this situation. However, Matthew does not tell us directly, while the report in Mark and Luke sticks to the clearer fact of what the people said.
I conclude that Mark and Luke make objective statements about what the people said. Matthew makes a subjective statement about what he understood from their praising God. I would lean toward this being a report of why he thought the crowd praised God, rather than his own reason for believing that God deserved praise.
Note: In dealing with this question, readers should also consider whether they think Matthew based his account on Mark's or vice versa, and/or whether either them were aware of Luke's versions. This site has several questions addressing this.