I did read the report, and I can help you out. The report doesn't say what VPM thinks it says, and it doesn't support what the MarketWatch article claims. (Note, the article drops the study at the beginning only to demonstrate that charitable giving is declining, and then uses other sources in an attempt to support the claim that a decline in religiosity is to blame.)
If you actually look into the numbers, however, you find some interesting things. For example, of all the religious groups listed, the one with the smallest decline in giving was the "Nones." Nones gave 1.21% of the income before the recession, compared to 1.19% after. All religious groups listed showed a larger decline, although the report notes that none of them are statistically significant.
Digging deeper, I noticed something else interesting. It appears above that VPM's theory (and C&C's, for that matter) is that religious folks are trained to give, so to speak, and so they give more even outside of church. However, the report separates religious and secular giving (importantly, "religious" giving is defined as giving directly to a religious congregation; more detail on that below), and thinking about those numbers raises some questions. For example, after the recession, the average household gives 0.82% to secular charities, and 2.19% to charity overall. Since the non-religious are giving 1.19% to charity, that means one of two things: they are either more generous than religious folks when it comes to secular charities, or they, despite being non-religious themselves, are giving a respectable amount of money to churches and synagogues, as well. Catholic families give 1.60%, higher than the average religious giving, but lower than the overall rate, while Protestants are giving 2.75%, higher than the overall rate.
The report does not break down charity type by socio-demographic group, so we can't draw any hard conclusions, but another citation in that article mentions that Catholics are giving less to their parish since the abuse scandal blew up again, which would explain their smaller number. Again, we can't decisively conclude anything, but we can speculate that it might very well be Protestants who are primarily driving religious gifts, the Nones who are primarily driving secular gifts, and the Catholics sort of filling a gray area.
At any rate, the study does nothing to support the contention that the correlation between religiosity and giving goes any further than the idea that religious folks give more because, in addition to regular charity, they also have churches to donate to, while the non-religious do not.
NB: Another question left unanswered is how much of the religious giving ends up going to the same purposes as secular giving. The report defines "religious" giving as all giving to religious congregations, and "secular" giving as all other giving. No doubt, some of that religious giving - which represents a large majority of all giving - is directed by various congregations to food, education, health, etc. Many Catholic parishes, for example, directly support Catholic education in order to help keep costs down for lower income families wishing to send children to Catholic schools.