That is only partially the case: yes, to some extent San Jose has a high homeless population for the same reason SF does (warm climate, access to transportation and social services, more lax enforcement of certain laws), but there are other causes that are unique to San Jose.

For example, since San Jose is much more car friendly, there are far more homeless people living in cars and RVs: many are employed, while the unemployed have often held working/middle-class jobs in the past. Some have been unemployed homeless since the collapse of the 2000 boom, others from the 2008 economic crisis and the real estate crisis (yes, a few had even home been home owners!).

San Jose was hard hit in the real estate crisis (though less so than some of California's exurbs), in that this is where people who long priced out of other areas (and most risk averse, for good reasons) bought at the very peak -- when it felt the "most safe" and the housing prices, while still high, were lower than those in other communities.