Your Professor is simplifying the question really. Acids/Bases are usually characterized by pKa values (-log of Ka) and as you can see here
http://evans.harvard.edu/pdf/evans_pka_table.pdfin the inorganic acids column strong acids have different values of pKa.
If you check the pKa values for HBr and HCl, they are respectively -9 and -8 (in water). The Ka in both cases is extremely high (10^9 and 10^8), so both completely dissociate. HBr dissociates a little more than HCl but the difference is negligible compared to the magnitude of their Ka's.
I think it's wrong to say all strong acids have the same strength, even though they completely dissociate. If you're just doing an exercise then it's alright to think that way, because for practical purposes you don't distinguish between the strength of HCl and HBr, but conceptually it's not exactly right.