Here is a simple explanation for your question: Rumen microbiota (bacteria 80%) accomplish ruminal digestion thru fermentation prcesses. The in sacco method depends on multiple factors but mainly on the activity of these microorganisms. Changes on the ruminal enviroment are going to affect this ferementation processes. So, the rate of the ruminal digestion of any component in the diet, is an indirect measurement of these microorganisms activity.
No need to add more to what the other responded wrote, except that the values obtained with the in sacco technique are very much dependent on the diet of the fistulated/cannulated animal. Another point, the in sacco technique is an open system (the in vitro is a closed system), then when the sample has tannins, in vitro may underestimate digestibility compared to what occurs in vivo
A couple of considerations in addition to the two good early responses
1. In in sacco determinations there is a 0 hour DM disappearance that has nothing to do with rumen microbiota per se, bur rather represent solubilization/loss of fine feed/forage particles. So far, I haven´t found a published correction for that in terms of actual rumen fermentation and generation of fermentation products. Dry matter disapearance after that point should more accurately represent rumen microbial fermentation of large feed/forage particles that didn´t escape thru the bag´s pores. Of course, corrections for that have been included in the in sacco method, mostly by using a large milling sieve and by using an uniform bag area to sample weight ratio. Yet, for some feed components such as minerals and protein, there is still a big zero-hour disappearance.
2. When quantifying protein disappearance/metabolism, it is ideal to estimate the contribution of bacterial protein, represented by bacteria and other rumen microbiota attached to the residue. This enables a closer estimate of feed true protein digestibility/rumen degradation