Well perhaps they should ask nicely then. In any case these men are arguidos, there are grounds to suspect them, the police has asked them hundreds of questions including did you kill Madeleine McCann. If the police have grounds to suspect them then they should be allowed to take a DNA sample and search their homes - in my opinion.
These requests are being done as nicely as possible. Those at the top of the investigation are skilled politicians. They work well with the leading Portuguese. This is evident by the progress -the digs, questioning, searching of cars.
All the rest is mid-level PJ sounding off and a former Home Secretary of Portugal having a moan about Portuguese sovereignty to get his name in the newspaper.
If requests are refused, it will be because they'll have been told to come back when they can provide corroborating evidence.. (which in itself, they will often receive some kind of warrant to go and find...).
I repeat, the FO have a good working relationship with Portugal and SY are savvy enough to do it the way the PT authorities want it done -- even if that takes forever.