I think the middle ground is being missed a bit here, and hopefully some are overstating their case.
First of all with regards to the original post. My assumption would be that the pilot had done engine runs and pre-flight checks earlier in the day. Without proof that he hadn't, I wouldn't be too quick to accuse him of poor airmanship.
Second. I have not owned an aircraft, but I fly both single pilot and multi crew in aircraft that only I or the one crew have flown for the last week. There are some basic things that must be done every day really. They include checking oil, correct fuel quantity, grade, and quality. Also the pitot needs to be checked clear and any orifices need to be checked clear of bird nest material and other contaminants.
In my opinion, a pre-flight check requires, at the very least, a walk-around, fluid check, and check of hatches and doors etc. I'd be doing this regardless of how many times I'd just flown the aeroplane. I can't do this just by glancing over the plane as I'm walking out to it, but it also doesn't take 30 minutes.
Having said that, there is no doubt, that someone who knows their aeroplane can do everything much more efficiently than someone who doesn't. This doesn't mean not doing stuff, it just means doing it a bit more quickly and probably focussing on the important bits rather than the stuff that doesn't change (such as control reversal checks when you flew it yesterday.)
As far as checks on the run go. It's easy to do that with two crew as one can look out while the other is looking in. While single pilot though, I think the least time heads down while taxiing, the better. Some checks require more heads down than others, so I find that there are some things I feel comfortable doing on the run (after landing clean-up,) and some things I don't (engine runs and before take-off checks.)
Ultimately it depends on your workload and what you are comfortable with. I don't think preferring to do checks while stopped is an indicator of "incompetance" or "inexperience" though. On the contrary, my experience is that the younger inexperienced guys who have been around just long enough to think they know what they're doing, are the most likely to try to be over efficient and do too many things at once.