What would be the point of tximport if you got the same thing as the genome-based alignment? Put another way, both alignment to the genome with subsequent counting and alignment to the transcriptome and then collapsing to the gene level are attempts to get at the same thing - the relative amount of transcript in a given sample for each gene. But we don't know how much transcript there is!

The fact that two different methods of estimating some underlying (unobserved) quantity don't necessarily agree doesn't invalidate either of them, because we don't know what the base truth is. If you want to believe that aligning to the genome and then generating counts is 'the right way to do things', then you should do that. If you are persuaded by Mike's paper that you get better results aligning to the transcriptome and then summarizing using tximport, then you should do that instead. But comparing the two and noting they are different doesn't tell you anything because the only reason for having a different method is because it's different than what came before.