Further, I'm not sure what the relationship of probabilities to the number of particles in the universe is. The probability of any given sequence emitted by hmmer as the "highest probability" is tiny (often 10e-50 or better, and for very good matches, 10e-138). So what's your point?
the work is mostly on okazaki fragments, but a major conclusion from my phd thesis was that B-RNA is stuck because of a very low probability event (the breaking of a large number of hbonds simultaneously).
Fine, then, a DNA-RNA base pair mismatch incurs approximately 1.5 kcal/mol penalty, which is a 1:10 less likelihood of matching. 3' UTRs of genes are what you need to reverse transcribe (by accident) the mRNA of interest to generate the cDNA you describe. On average they are around 700 bp, the odds of finding an exact match are about 700/4^18 - then a one bp mismatch is 700/4^17 times a 1:10 hit in terms of competitive binding. Two bp mismatch is 700/4^16 times 1:100. Then you have to consider that it's evolutionarily unlikely to have segments that exactly or inexactly match tRNAs because the resulting dsRNA is likely to engage in silencing via the DROSHA mechanism - probably because our bodies like to guess what - get rid of ssRNA viruses. So these numbers are probably at least on the order of 1:10 or even 1:100 or more in the wrong direction.
and yet, existence proofs demonstrate you are wrong. Again, re-read the section on virus tumor oncogenes in The Biology of Cancer; pretty much everythign we know about oncogenes came from this physical mechanism.