No, no. You are going in the right direction in analysing the morality of such proclamation. The point is, you can a) give others and collect reward in terms of other's people perception/rewarding of you (what the Bible passage above suggests is bad), b) do the same because someone just convinced you you'll get a reward from .. someone important, worthy of respect/awe (what the passage suggests is good, though I'm sure there will be those who say it's just parabole for being humble in giving, which of course the text could say but somehow doesn't), c) for some another reason. We'll get to c) in a minute.
When you think about what this is really easy to see is a = b. That I am rewarded with promise of heaven for a deed, or hope of being well-respected by others who see what I've done, affects the same object: ego. It's not driven by desire to help others (compassion, love or else), but desire to be seen /judged as good by others.
There is a c) (and more for sure). The much more mundane reason c) is "give to people and let your reward be the feeling you get that you do a good thing". Good thing can be in this case simply the result of mental congruence of your act with, say, your utilitarian belief that "helping others by decreasing their suffering is good".
If I tell people "a good act is when you help others to help them maximize utility", it's a moral stance. It's a very different moral stance than "a good act is when you do what someone says you should do in order to get eternal life".
The former is far better from ego-point of view, and less prone to corruption, and focuses on the values and reasons why somethign is good, in other words - promotes understanding and is clear why it's good. The latter promotes blind following and subservience to anothe person/being becomgin the guide of y our actions.
It's clear that most people need a guide, but be careful what kind of guide you pick.