its a relative question, depends upon research question in hand and address in the software. Read related publication of the software and compare your data. You can confirm reliability in few cases by already knowing you own data.

But at the end of the day, they all are statical analysis, bases on statistical modeling of the given problem. So its all Statistics

True, as I already said! its Statistics and in statistics reliability is always relative to your confident interval. Removing bias is very critical in the process also watch out inherited bias, instrument dependent etc. you will find out many publication on bias remove issue.

You both are right but the problem is we just put a chip inside the machine and after that we rely fully what machine provides us.......i think there should be softwares fr cross checking

That part has been taken care by vender specific data acquisition software. You can find any irregularities in data pre-processing step.

I recommend you to read about sequencing technology and different type of sequencing machines.

you're right to question the backend of any software program.

For commerical software you wont have access to the source so you'll have to trust them.

For the vast amount of work people are doing the software is very reliable - the calculation is simple it purely a difference between means of two sets of arrays followed by a t-test and multiple testing correction - it is highly unlikely that there will be a mistakes here. No the other hand if commerical software offers machine learning options you should be careful with these.

For open source packages in R namely the bioconductor packages you can view the operations behind the method no problem.