"And he shall surely heal" - the permission or obligation to provide medical treatment

וְכִֽי־יְרִיבֻ֣ן אֲנָשִׁ֔ים וְהִכָּה־אִישׁ֙ אֶת־רֵעֵ֔הוּ בְּאֶ֖בֶן א֣וֹ בְאֶגְרֹ֑ף וְלֹ֥א יָמ֖וּת וְנָפַ֥ל לְמִשְׁכָּֽב׃

Exodus 21:18

When [two] parties quarrel and one strikes the other with stone or fist, and the victim does not die but has to take to bed.

שמות כ״א:י״ט

אִם־יָק֞וּם וְהִתְהַלֵּ֥ךְ בַּח֛וּץ עַל־מִשְׁעַנְתּ֖וֹ וְנִקָּ֣ה הַמַּכֶּ֑ה רַ֥ק שִׁבְתּ֛וֹ יִתֵּ֖ן וְרַפֹּ֥א יְרַפֵּֽא׃ (ס)

Exodus 21:19

if that victim then gets up and walks outdoors upon a staff, the assailant shall go unpunished—except for paying for the idleness and the cure. (Rapo yirape, in Hebrew - sometimes translated, "He shall surely heal..."

According to your first reading of these verses, who is obligated to do what for whom?

בבא קמא פ״ה א:ט״ו

וּלְרַבָּנַן בָּתְרָאֵי, דְּאָמְרִי: כֹּל שֶׁחַיָּיב בְּשֶׁבֶת – חַיָּיב בְּרִיפּוּי, וְכֹל שֶׁאֵינוֹ חַיָּיב בְּשֶׁבֶת – אֵינוֹ חַיָּיב בְּרִיפּוּי; רִיפּוּי דִּתְנָא בֵּיהּ קָרָא – לְמָה לִי? מִיבְּעֵי לֵיהּ לְכִדְתָנָא דְּבֵי רַבִּי יִשְׁמָעֵאל – דְּתַנְיָא, דְּבֵי רַבִּי יִשְׁמָעֵאל אוֹמֵר: ״וְרַפֹּא יְרַפֵּא״ – מִכָּאן שֶׁנִּיתַּן רְשׁוּת לָרוֹפֵא לְרַפּאוֹת.

Bava Kamma 85a:15

The Gemara asks: And according to the opinion of the latter Rabbis in the baraita, who say: Anyone who is liable to pay compensation for loss of livelihood is liable to pay compensation for medical costs, and anyone who is not liable to pay compensation for loss of livelihood is not liable to pay compensation for medical costs, why do I need, i.e., how do I account for, the fact that the verse repeated the obligation to pay medical costs? (i.e. why is the root r.p.a. repeated Rapo yirape?) The Gemara answers: It is necessary for that which the school of Rabbi Yishmael taught. As it is taught in a baraita that the school of Rabbi Yishmael says: When the verse states: “And shall cause him to be thoroughly healed [verappo yerappe]” (Exodus 21:19), it is derived from here that permission is granted to a doctor to heal, and it is not considered to be an intervention counter to the will of God.

How does this text change the understanding of the original verse? Why wouldn't we be allowed to heal?

בעיות הלכתיות עכשוויות, כרך ב, חלק ראשון, פרק ג: שאלות רפואיות ד׳

...

Contemporary Halakhic Problems, Vol II, Part I, Chapter III Medical Questions 4

The obligation to render medical assistance flows from multiple scriptural sources and a person who renders such aid fulfills a number of diverse mizvot. Perhaps the most widely quoted source is the statement found in Baba Kamma 85a: " 'And he shall cause him to be thoroughly healed' (Exodus 21:20)—from here [it is derived] that the physician is granted permission to heal." Ramban, in his authoritative halakhic work, Torat ha-Adam, comments that the "permission" or "dispensation" of which the Gemara speaks in actuality constitutes a commandment or obligation ("Hai reshut, reshut de-mizvah hi"). Thus the medical practitioner is not merely permitted, but is required, to render aid.

How do we get from permission to heal to an obligation to do so?

תרגום אונקלוס על שמות כ״א:י״ט

אִם יְקוּם וִיהַלִיךְ בְּבָרָא עַל בּוּרְיֵהּ וִיהֵי זַכָּאָה מָחְיָא לְחוֹד בּוּטְלָנֵהּ יִתֵּן וַאֲגַר אַסְיָא יְשַׁלֵם:

Onkelos Exodus 21:19

If he gets up and is able to walk on the outside on his own power, the one who struck him shall be acquitted. Still he must pay for his loss of work, and must pay for his complete cure [the doctor’s fee].

מכילתא דרבי ישמעאל, מַסֶּכְתָּא דִנְזִיקִין ו׳:א׳

(שמות כא,יח) "וְכִי יְרִיבֻן אֲנָשִׁים, וְהִכָּה אִישׁ אֶת רֵעֵהוּ בְּאֶבֶן אוֹ בְאֶגְרֹף, וְלֹא יָמוּת וְנָפַל לְמִשְׁכָּב." לָמָּה נֶאֶמְרָה פָּרָשָׁה זוֹ? לְפִי שֶׁהוּא אוֹמֵר: (שמות כא,כד) "עַיִן תַּחַת עַיִן, שֵׁן תַּחַת שֵׁן, יָד תַּחַת יָד, רֶגֶל תַּחַת רָגֶל." אֲבָל שֶׁבֶת וְרִפּוּי לֹא שָׁמַעְנוּ! תִּלְמֹד לוֹמַר "וְכִי יְרִיבֻן אֲנָשִׁים, וְהִכָּה אִישׁ אֶת רֵעֵהוּ בְּאֶבֶן אוֹ בְאֶגְרֹף, וְלֹא יָמוּת וְנָפַל לְמִשְׁכָּב." (שמות כא,יט) "אִם יָקוּם וְהִתְהַלֵּךְ בַּחוּץ עַל מִשְׁעַנְתּוֹ, וְנִקָּה הַמַּכֶּה, רַק שִׁבְתּוֹ יִתֵּן וְרַפֹּא יְרַפֵּא." בָּא הַכָּתוּב לְלַמֵּד בּוֹ דְּבָרִים הַמְחֻסָּרִים בּוֹ.

Mekhilta DeRabbi Yishmael, Tractate Nezikin 6:1

(Exodus 21:18) "And if men quarrel": What is the intent of this section? It is written (Ibid. 21:24) "an eye for an eye," but sheveth (work-disability payment) and ripui (medical expenses) are not mentioned. It is, therefore, written (Ibid. 19) "If he arise, etc." Scripture comes to teach of (other payments) that are due him.

What other obligations go along with the obligation to heal? Who is obligated to fulfill them?

חובות הלבבות, שער רביעי - שער הביטחון ד׳:ל״ז

וכן נאמר בענין הבריאות והחלי כי על האדם לבטח בבורא בזה ולהשתדל בהתמדת הבריאות בסבות אשר מטבען זה ולדחות המדוה במה שנהגו לדחותו כמו שצוה הבורא יתעלה (שמות כא יט) ורפא ירפא מבלי שיבטח על סבות הבריאות והחלי שהן מועילות או מזיקות אלא ברשות הבורא.

Duties of the Heart, Fourth Treatise on Trust 4:37

Similarly, we will say regarding health and sickness. A man is placed under a duty to trust in the Creator in this, while working on maintaining his health according to the means whose nature promotes this, and to fight sickness according to the customary ways, as the Creator commanded "and he shall surely heal him" (shmos 21:19). All of this, without trusting in the means of health or illness that they could help or hurt without the permission of the Creator.

פלא יועץ של״ה:א׳

רפואה - אמרו רבותינו זכרונם לברכה (שמות כא יט) ורפא ירפא. מכאן שנתנה תורה רשות לרופא לרפאות (ברכות ס א). ועוד אמרו על הפסוק (דברים כח נט): וחלים רעים ונאמנים. שהם נאמנים בשליחותן (רש"י שם), שבשעה ששולחין אותן גוזרים עליהם שלא יצאו אלא ביום פלוני, ביד פלוני, על ידי סם פלוני (ילקוט שמעוני יתרו רמז רפט). ועוד אמרו רבותינו זכרונם לברכה (סנהדרין יז ב), שלא ידור אדם במקום שאין רופא:

Pele Yoetz 335:1

Healing - Our sages of blessed memory said on the verse "And heal he will be healed" [shemot 21;19] - from here the Torah gave the permission to doctors to heal. [berakhot 60a] And it is also said [with respect to illnesses] - that they are bad and trustworthy [Deut / devarim 28;59] - that they are "trustworthy" as an emissary / delegate [of heaven] [rashi there] for at the time that they are appointed / delegated [to fall upon a person] - it is decreed upon them that they should only leave on a determined day by the appointed doctor using the prescribed medicine. Our sages have also said "A person should not live in a place where there is no doctor" [sanhedrin 17b]

How do these two sources (one from medieval Spain, the other from 19th century Bulgaria) reconcile the employment of medical doctors with ultimate faith in God?