Although those two pieces of advice seem contradictory, there is a sound reason behind them.
White bread, made from white flour, has more or less the same glycaemic response curve as sugar. Eating white bread will affect your BG levels as sure as eating granulated sugar by the spoonful. Brown bread however is a vague term, essentially meaningless in the UK.
Even if the curve was the same shape there is considerably more glucose in the bread. So it would cause a greater rise.
In practice the curve is unlikely to be the same since white bread is high GI, whereas sucrose is medium GI.
Bread which is made from flour which contains the entire contents of the whole grain is a lot more than just the highly refined endosperm found in white flour. For example, some of the carbohydrates are cellulose based and indigestible. We call it roughage or dietary fibre. Whole grain flour also contains more complex carbohydrates which take much longer to break down than the highly refined white flour.
Complexity of carbohydrates is not a factor in digestion of carbohydrates.
The most complex, amylopectin, is very quick and easy to digest. Amylose, the next most complex, is rather "interesting". Depending on the exact physical form of the molecule it can either be a little harder to digest than amylopectin or a type of fibre. Maltodextrins are also quick and easy to digest (indeed they produced as an intermediate product of the digestion of either amylopectin or amylose.)
Galactan hydrolises to galactose in an acid (or alkaline) environment.
Which other "complex carbohydrates" do you think the human digestive system is able to hydrolyse? Any which can't be are, by definition, "fibre".
With disaccharides maltose will be hydrolysed before sucrose or lactose. Glucose, fructose and galactose don't need any digestion.
However, most bread in the UK, even though it is described as wholemeal or wholegrain, is not. Waitrose's wholemeal bread contains only 6% wholemeal and 51% white flour. It also contains 43% of other things!
Essentially the only way you can trust bread to be wholemeal is to bake it yourself or find a baker who bakes real bread.
You'd also need to check if your "wholegrain flour" actually is what you think it is. (Remember that most "whole milk" is actually skimmed milk with cream added back in...)
Be careful though because a lot of them do things like add molasses to the mix.
Which may reduce the GI. Adding "sugar" a "starchy food" can do this. Since it means there will, in effect, be less glucose per unit mass of the resultant mix. This would be most effective if the sugar was fructose or galactose. But still significent with sucrose or lactose. (Possibly detectable using glucose or maltose.) Obvious looking at the chemistry. But appears to surprise quite a few people. But then so does the fact that "starch" is made up of lots of glucose molecules packed together. Which is why these kind of foods tend to be "worst than sugar" from the diabetic POV. Since all glucose in the gut goes into the blood. Regardless of if started out as "just glucose" or part of maltose, sucrose; lactose; amylose or amylopectin. (In contrast fructose and galactose get removed, from the blood, very quickly by the liver.)