Actually, I haven’t seen that said as a broad generalization – more along the lines of references to specific schools, or references to merit aid. Transfer students are of course entitled to federally based aid (loans, work-study, Pell grants for low income) — and need based aid depends on the policy of the school. For example, my daughter’s alma mater provides full need-based aid to fall transfers, but not to students transferring in for spring semester. I’m sure that’s a budget thing; I know that students who apply are clearly informed of that policy.
The big difference is that merit money is a lot harder to get as an incoming transfer – and that is where more generalized statements are made. I’ve seen it come up where students are wondering whether they can save money by first attending a community college or local commuter school for two years, then transferring to their preferred college.
I think most colleges that provide need-based aid also will provide it to at least some transfer students, but typically with some restrictions or limitations. This would include schools that provide the aid but don’t guarantee to meet full need.