The problem is that different government agencies have entirely different definitions as to what constitutes 'residency'. The Texas DPS (DMV equivalent) has different rules compared to the IRS, which has different rules compared to Texas Universities (for tuition purposes), etc. It is indeed a grey area, which is exacerbated by the fact that there are 50 states, each with different rules and laws.

Which is why my opinion is, don't worry too much about it: maintain your drivers licenses, banks accounts and credit cards where it is reasonably easy for you to do so, as that will only be advantageous to you in the long run. If it is too much effort to renew a license (say for a US expat living 100% in a foreign country with no US address that the license can be mailed to), then don't bother. I really don't think it is a huge issue to have a license mailed to, say, your brother's apartment in Dallas.

As an expat living in Dubai, this would be the least of your issues when it comes to dealing with government bureaucracy anyhow (for anybody who has ever complained about waiting in line to get a driving license in the US, try getting ANY government service in the UAE).