It doesn't matter who owns the vehicles / carriages, what matters is the route and the service.

Basically you cannot take any trains marked IC, EC, ICE on timetables, maps and information boards. (Although there are a handful of exceptions.)

You can take local and regional trains which are marked R, RB, RE, REX, S, U, maybe a few other letters. They are slower and stop more often and have fewer facilities on board. If a day ticket for the area's transport network would be valid, then it will also be valid with the €49 ticket.

Some regional transport networks extend slightly into neighbouring countries, so in some cases you can use the €49 ticket to travel across the border, but not very far. For example you can go to Salzburg (Austria), Wissembourg (France), Świnoujście (Poland), Basel (Switzerland), Luxembourg - on regional trains/buses only.

While there is an RB train that goes from Saxony to Děčín in Czechia, the arrangement there is that the local VVO tickets are only valid up to the final stop in Germany (unless you buy a special cross-border ticket). Therefore the same applies to the €49 ticket.

The train from Prague to Berlin is EC so the €49 ticket is not valid on it no matter which country you are in. What the first response was trying to say is that, to save money you could just buy a separate ticket from Prague to the first stop in Germany, which is usually Bad Schandau. This might be cheaper than going all the way to Dresden on the EC. (If the ticketing arrangement on the Czech border was similar to that on the Austrian border, then you might be able to use some Czech offer to only pay up to Děčín and then use the €49 ticket from there, but unfortunately this is not the case.)

Then you can use the €49 ticket on the RE20 from Bad Schandau to Dresden, then the RE50 to Leipzig and so on, which will be slower, but that's the point.