Ah, it's the famous ochazuke (not ocha/tea) story of Kyoto!
I don't think you should be worried (or offended) about the tea offered to you during your stay in Kyoto.
I'm from Tokyo and to me (and most of non-Kyotolites) Kyoto is a great city with a long history, and people are very conservative and very proud of themselves and Kyoto.
I've heard that people who moved in Kyoto and have lived there for more than 10 years, are still regarded by the locals as "outsider" (or non-Kyotolites).
The story about ochazuke (which is called "bubuzuke" there) is, when the guest is staying for long hours, they offer ochazuke saying "bubuzuke demo ikaga dosuka?" (how about something like ochazuke?) implying "it's getting late and time for supper, so you'd better leave now".
According to the stories I've read/heard, if the people don't take the hint and take the phrase literally instead and accept the offer "thank you, I'd like to have some, then" etc., they'd laugh at the "country bumpkins who do not know the mammer" behind their backs.
*How much this is still in practice, I have no idea. Maybe it used but not any more with younger generations.
My guess is for them being straight forward is rude and prefer the round-about way of saying something. Maybe it originally came from the politeness (i.e. consideration not to offend others by saying things too directly). But it's a local code, not universal and mostly not understood by the people from other places, for "strangers" from Kyotolites' perspective this offering-ochazuke-ritual does not work well and became the source of cultural gap conflicts(?) between Kyotolites vs outsiders (yosomono)...
The above statement about Kyotolites is general image people hold, not that all or most of the poeple in Kyoto are so mean and against non-Kyotolites. ;-)