Bhu faking cancer seems too probable as she wants to ascertain her position at any cost; she has already done this once before by using Lax's weakness and separating TPS from Lax. As others feel too, in large hospitals, drs do rely on the blood reports/other reports to base their decisions, and for Bhu with the entire hospital in her hands it is not a big deal to mess up and change the reports. This is quite evident from her letter where she clearly is turning the tables against TPS and she had to bring out the reality abt T so she can prove abt TPS. A fake sorry for T too just so T no longer is against Bhu! Her mean character is clearly evident in this letter. A person who indeed has cancer and knows she would die would atleast genuinely repent for their sins which is completely absent in the letter. She has made a smart move and has struck back with vengeance. Well, Lax is a complete fool and a loser. TPS is correct when she says that if Lax were loyal to her, no matter what Bhu's moves were, Bhu cud not have done anything.
Also, I too am of the opinion that T meant no revenge when she sent TPS to Lax's house as she felt she could at least do some justice to TPS for what Bhu did to her. T felt that TPS shud fight for what is rightfully hers instead of letting go off both easily. T is not going to gain a penny by sending TPS to Lax's house and she just wanted Bhu to undergo the same suffering that TPS had to go thru her entire life. Also, T wanted to show Bhu her actual position and status; T wanted to show Bhu that whatever she boasts of doesn't belong to hers. Also, Bhu didn't seem to have any sort of guilt even after knowing T as her own blood but was out to almost kill her! iF BHU had remained aloof from T or not had any dealings with her, T wud not have gone to this extent. ( well, C almost did the same thing to T by trying to brainwash TA against T, but T was not going to give up easily and TA too was loyal to T!) I don't think T used TPS; TPS is not a stranger to Lax and she too was wronged by Bhu and waiting for a chance to teach her a lesson. Also for T/TPS this was the best way to strip Bhu of her wealth and in turn her arrogance easily.