That's all I've attempted to do. To say it doesn't "match" extant demonstrations is really not a totally accurate statement; a more accurate statement would be that the fossil record doesn't (usually) provide enough information in and of itself to draw gross conclusions about the nature of minute evolutionary changes one way or the other.
These minute changes are the only demonstrable "evolution".
This is the only direct evolution we observe, true; but the consequences of evolutionary theory are observable on many more lines of evidence than just microevolutionary adaptation/change and the fossil record provide. Morphological similarities and variations amongst related species and biogeographical distribution provide a wealth of information. With the advent of genome sequencing, direct tests can also be made using statistical mutation rates to see how long distinct lineages have been separate.
the fossil record, records dead things, the so-called "evolutionary chain" is one explanation (granted the most conventionally excepted explination) of the fossil record.
I know of no other scientific explanation that provides such a consistent model of life.
the bible told of mass extinction long before man (tried to divide it up into 6-7 mass extinctions)found the fossil record.
There are definitely multiple mass extinctions in the past, the Permian extinction being the most catastrophic. This knowledge is provided by extant geological evidence pointing to the strata where the relevant fossils are found. (Again, other lines of inquiry seem to point to the same conclusions...)