You are principly correct ...
But I need to remind that the residence card is cross referenced to the passport.
So, it may cause a problem if the residence card is cross referenced to the lost passport !
Although usually only the residence card is checked on internal Schengen travel having a passport number different from the one on the (newly issued) passport is not a good idea ...
Some Schengen residence cards are not cross-referenced to a passport, lost or otherwise.
A lot of US citizens resident in the Schengen zone with residence cards still get their US passports stamped on many, most or even all of their entries to and exits from the Schengen zone even when showing a residence card or resident visa permit sticker (some of which are still out there too).